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Book SynopsisAbout our authors Robert L. Gould (Ph.D., University of California - San Diego) is a leader in the statistics education community. He has served as chair of the AMATYC/ASA joint committee, was co-leader of the Two-Year College Data Science Summit hosted by the American Statistical Association, served as chair of the ASA's Statistics Education Section, and was a co-author of the 2005?Guidelines for Assessment in Instruction on Statistics Education (GAISE) College Report. While serving as the Associate Director of Professional Development for CAUSE (Consortium for the Advancement of Undergraduate Statistics Education), he worked closely with the American Mathematical Association of Two-Year Colleges (AMATYC) to provide traveling workshops and summer institutes in statistics. He was the lead principal investigator of the NSF-funded Mobilize Project, which developed and implemented the first high-school level data science course. For over 20 years, he Table of Contents1. Introduction to Data 1.1 What Are Data? 1.2 Classifying and Storing Data 1.3 Investigating Data 1.4 Organizing Categorical Data 1.5 Collecting Data to Understand Causality 2. Picturing Variation with Graphs 2.1 Visualizing Variation in Numerical Data 2.2 Summarizing Important Features of a Numerical Distribution 2.3 Visualizing Variation in Categorical Variables 2.4 Summarizing Categorical Distributions 2.5 Interpreting Graphs 3. Numerical Summaries of Center and Variation 3.1 Summaries for Symmetric Distributions 3.2 What's Unusual? The Empirical Rule and z-Scores 3.3 Summaries for Skewed Distributions 3.4 Comparing Measures of Center 3.5 Using Boxplots for Displaying Summaries< 4. Regression Analysis: Exploring Associations between Variables 4.1 Visualizing Variability with a Scatterplot 4.2 Measuring Strength of Association with Correlation 4.3 Modeling Linear Trends 4.4 Evaluating the Linear Model 5. Modeling Variation with Probability 5.1 What Is Randomness? 5.2 Finding Theoretical Probabilities 5.3 Associations in Categorical Variables 5.4 Finding Empirical Probabilities 6. Modeling Rando Events: The Normal and Binomial Models 6.1 Probability Distributions Are Models of Random Experiments 6.2 The Normal Model 6.3 The Binomial Model (Optional) 7. Survey Sampling and Inference 7.1 Learning about the World through Surveys 7.2 Measuring the Quality of a Survey 7.3 The Central Limit Theorem for Sample Proportions 7.4 Estimating the Population Proportion with Confidence Intervals 7.5 Comparing Two Population Proportions with Confidence 8. Hypothesis Testing for Population Proportions 8.1 The Essential Ingredients of Hypothesis Testing 8.2 Hypothesis Testing in Four Steps 8.3 Hypothesis Tests in Detail 8.4 Comparing Proportions from Two Populations 9. Inferring Population Means 9.1 Sample Means of Rando Samples 9.2 The Central Limit Theorem for Sample Means 9.3 Answering Questions about the Mean of a Population 9.4 Hypothesis Testing for Means 9.5 Comparing Two Population Means 9.6 Overview of Analyzing Means 10. Associations between Categorical Variables 10.1 The Basic Ingredients for Testing with Categorical Variables 10.2 The Chi-Square Test for Goodness of Fit 10.3 Chi-Square Tests for Associations between Categorical Variables 10.4 Hypothesis Tests When Sample Sizes Are Small 11. Multiple Comparisons and Analysis of Variance 11.1 Multiple Comparisons 11.2 The Analysis of Variance 11.3 The ANOVA Test 11.4 Post-Hoc Procedures 12. Experimental Design: Controlling Variation 12.1 Variation Out of Control 12.2 Controlling Variation in Surveys 12.3 Reading Research Papers 13. Inference without Normality 13.1 Transforming Data 13.2 The Sign Test for Paired Data 13.3 Mann-Whitney Test for Two Independent Groups 13.4 Randomization Tests 14. Inference for Regression 14.1 The Linear Regression Model 14.2 Using the Linear Model 14.3 Predicting Values and Estimating Means

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Book Synopsis

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Book SynopsisThis book covers all the latest advances, as well as more established methods, in the application of statistical and optimisation methods within modern industry. These include applications from a range of industries that include micro-electronics, chemical, automotive, engineering, food, component assembly, household goods and plastics.Trade Review"The book can be recommended to any interested in the application of statistical methods in business." (Statistical Papers, 6 July 2011) Table of ContentsContents Contributors Preface 1 Introduction Shirley Coleman, Tony Fouweather and Dave Stewardson 2 A History of Industrial Statistics Jeroen de Mast 3 Statistical Consultancy 3.I A Statistician in Industry Ronald J.M.M. Does and Albert Trip 3.II Black Belt Types Roland Caulcutt 3.III Statistical Consulstancy Units at Universities Ronald J.M.M. Does and András Zempléni 3.IV Consultancy? . . . What's in It for Me? Roland Caulcutt 4 The Statistical Efficiency Conjecture Ron S. Kenett, Anne De Frenne, Xavier Tort-Martorell and Chris McCollin 5 Management Statistics Irena Ograjenšek and Ron S. Kenett 6 Service Quality Irena Ograjenšek 7 Design and Analysis of Industrial Experiments Timothy J. Robinson 8 Data Mining Paola Cerchiello, Silvia Figini and Paolo Giudici 9 Using Statistical Process Control for Continual Improvement Donald J. Wheeler and Øystein Evandt 10 Advanced Statistical Process Control Murat Kulahci and Connie Borror 11 Measurement System Analysis Giulio Barbato, Grazia Vicario and Raffaello Levi 12 Safety and Reliability 12.I Reliability Engineering: The State of the Art Chris McCollin 12.II Stochastics for the Quality Movement: An Integrated Approach to Reliability and Safety M. F. Ramalhoto 13 Multivariate and Multiscale Data Analysis Marco P. Seabra dos Reis and Pedro M. Saraiva 14 Simulation in Industrial Statistics David R´ıos Insua, Jorge Muruzabal, Jes´us Palomo, Fabrizio Ruggeri, Julio Holgado and Ra´ul Moreno 15 Communication Tony Greenfield and John Logsdon Index

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Book SynopsisTable of ContentsA Note to Students from the Authors vii1 A CASE STUDY OF STATISTICS IN ACTION 2 2 EXPLORING DISTRIBUTIONS 22 3 RELATIONSHIPS BETWEEN TWO QUANTITATIVE VARIABLES 100 4 SAMPLE SURVEYS AND EXPERIMENTS 208 5 SAMPLING DISTRIBUTIONS 266 6 PROBABILITY MODELS 326 7 PROBABILITY DISTRIBUTIONS 378 8 INFERENCE FOR PROPORTIONS 412 9 INFERENCE FOR MEANS 478 10 CHI-SQUARE TESTS 576 11 INFERENCE FOR REGRESSION 628 12 STATISTICS IN ACTION: CASE STUDIES 678 Appendix: Statistical Tables 699 Table A: Standard Normal Probabilities 699 Table B: t-Distribution Critical Values 701 Table C: Chi-Square Distribution Critical Values 702 Table D: Random Digits 703 Glossary 704 Brief Answers to Selected Problems 712 Index 743 Photo Credits 752

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Book SynopsisMaintaining the same accessible and hands-on presentation, Introductory Biostatistics, Second Edition continues to provide an organized introduction to basic statistical concepts commonly applied in research across the health sciences.Table of ContentsPreface to the Second Edition xiii Preface to the First Edition xv About the Companion Website xix 1 Descriptive Methods for Categorical Data 1 1.1 Proportions 1 1.1.1 Comparative Studies 2 1.1.2 Screening Tests 5 1.1.3 Displaying Proportions 7 1.2 Rates 10 1.2.1 Changes 11 1.2.2 Measures of Morbidity and Mortality 13 1.2.3 Standardization of Rates 15 1.3 Ratios 18 1.3.1 Relative Risk 18 1.3.2 Odds and Odds Ratio 18 1.3.3 Generalized Odds for Ordered 2 × k Tables 21 1.3.4 Mantel–Haenszel Method 25 1.3.5 Standardized Mortality Ratio 28 1.4 Notes on Computations 30 Exercises 32 2 Descriptive Methods for Continuous Data 55 2.1 Tabular and Graphical Methods 55 2.1.1 One‐Way Scatter Plots 55 2.1.2 Frequency Distribution 56 2.1.3 Histogram and Frequency Polygon 60 2.1.4 Cumulative Frequency Graph and Percentiles 64 2.1.5 Stem and Leaf Diagrams 68 2.2 Numerical Methods 69 2.2.1 Mean 69 2.2.2 Other Measures of Location 72 2.2.3 Measures of Dispersion 73 2.2.4 Box Plots 76 2.3 Special Case of Binary Data 77 2.4 Coefficients of Correlation 78 2.4.1 Pearson’s Correlation Coefficient 80 2.4.2 Nonparametric Correlation Coefficients 83 2.5 Notes on Computations 85 Exercises 87 3 Probability and Probability Models 103 3.1 Probability 103 3.1.1 Certainty of Uncertainty 104 3.1.2 Probability 104 3.1.3 Statistical Relationship 106 3.1.4 Using Screening Tests 109 3.1.5 Measuring Agreement 112 3.2 Normal Distribution 114 3.2.1 Shape of the Normal Curve 114 3.2.2 Areas Under the Standard Normal Curve 116 3.2.3 Normal Distribution as a Probability Model 122 3.3 Probability Models for Continuous Data 124 3.4 Probability Models for Discrete Data 125 3.4.1 Binomial Distribution 126 3.4.2 Poisson Distribution 128 3.5 Brief Notes on the Fundamentals 130 3.5.1 Mean and Variance 130 3.5.2 Pair‐Matched Case–Control Study 130 3.6 Notes on Computations 132 Exercises 134 4 Estimation of Parameters 141 4.1 Basic Concepts 142 4.1.1 Statistics as Variables 143 4.1.2 Sampling Distributions 143 4.1.3 Introduction to Confidence Estimation 145 4.2 Estimation of Means 146 4.2.1 Confidence Intervals for a Mean 147 4.2.2 Uses of Small Samples 149 4.2.3 Evaluation of Interventions 151 4.3 Estimation of Proportions 153 4.4 Estimation of Odds Ratios 157 4.5 Estimation of Correlation Coefficients 160 4.6 Brief Notes on the Fundamentals 163 4.7 Notes on Computations 165 Exercises 166 5 Introduction to Statistical Tests of Significance 179 5.1 Basic Concepts 180 5.1.1 Hypothesis Tests 181 5.1.2 Statistical Evidence 182 5.1.3 Errors 182 5.2 Analogies 185 5.2.1 Trials by Jury 185 5.2.2 Medical Screening Tests 186 5.2.3 Common Expectations 186 5.3 Summaries and Conclusions 187 5.3.1 Rejection Region 187 5.3.2 p Values 189 5.3.3 Relationship to Confidence Intervals 191 5.4 Brief Notes on the Fundamentals 193 5.4.1 Type I and Type II Errors 193 5.4.2 More about Errors and p Values 194 Exercises 194 6 Comparison of Population Proportions 197 6.1 One‐Sample Problem with Binary Data 197 6.2 Analysis of Pair‐Matched Data 199 6.3 Comparison of Two Proportions 202 6.4 Mantel–Haenszel Method 206 6.5 Inferences for General Two‐Way Tables 211 6.6 Fisher’s Exact Test 217 6.7 Ordered 2 × K Contingency Tables 219 6.8 Notes on Computations 222 Exercises 222 7 Comparison of Population Means 235 7.1 One‐Sample Problem with Continuous Data 235 7.2 Analysis of Pair‐Matched Data 237 7.3 Comparison of Two Means 242 7.4 Nonparametric Methods 246 7.4.1 Wilcoxon Rank‐Sum Test 246 7.4.2 Wilcoxon Signed‐Rank Test 250 7.5 One‐Way Analysis of Variance 252 7.5.1 One‐Way Analysis of Variance Model 253 7.5.2 Group Comparisons 258 7.6 Brief Notes on the Fundamentals 259 7.7 Notes on Computations 260 Exercises 260 8 Analysis of Variance 273 8.1 Factorial Studies 273 8.1.1 Two Crossed Factors 273 8.1.2 Extensions to More Than Two Factors 278 8.2 Block Designs 280 8.2.1 Purpose 280 8.2.2 Fixed Block Designs 281 8.2.3 Random Block Designs 284 8.3 Diagnostics 287 Exercises 291 9 Regression Analysis 297 9.1 Simple Regression Analysis 298 9.1.1 Correlation and Regression 298 9.1.2 Simple Linear Regression Model 301 9.1.3 Scatter Diagram 302 9.1.4 Meaning of Regression Parameters 302 9.1.5 Estimation of Parameters and Prediction 303 9.1.6 Testing for Independence 307 9.1.7 Analysis of Variance Approach 309 9.1.8 Some Biomedical Applications 311 9.2 Multiple Regression Analysis 317 9.2.1 Regression Model with Several Independent Variables 318 9.2.2 Meaning of Regression Parameters 318 9.2.3 Effect Modifications 319 9.2.4 Polynomial Regression 319 9.2.5 Estimation of Parameters and Prediction 320 9.2.6 Analysis of Variance Approach 321 9.2.7 Testing Hypotheses in Multiple Linear Regression 322 9.2.8 Some Biomedical Applications 330 9.3 Graphical and Computational Aids 334 Exercises 336 10 Logistic Regression 351 10.1 Simple Regression Analysis 353 10.1.1 Simple Logistic Regression Model 353 10.1.2 Measure of Association 355 10.1.3 Effect of Measurement Scale 356 10.1.4 Tests of Association 358 10.1.5 Use of the Logistic Model for Different Designs 358 10.1.6 Overdispersion 359 10.2 Multiple Regression Analysis 362 10.2.1 Logistic Regression Model with Several Covariates 363 10.2.2 Effect Modifications 364 10.2.3 Polynomial Regression 365 10.2.4 Testing Hypotheses in Multiple Logistic Regression 365 10.2.5 Receiver Operating Characteristic Curve 372 10.2.6 ROC Curve and Logistic Regression 374 10.3 Brief Notes on the Fundamentals 375 10.4 Notes on Computing 377 Exercises 377 11 Methods for Count Data 383 11.1 Poisson Distribution 383 11.2 Testing Goodness of Fit 387 11.3 Poisson Regression Model 389 11.3.1 Simple Regression Analysis 389 11.3.2 Multiple Regression Analysis 393 11.3.3 Overdispersion 402 11.3.4 Stepwise Regression 404 Exercises 406 12 Methods for Repeatedly Measured Responses 409 12.1 Extending Regression Methods Beyond Independent Data 409 12.2 Continuous Responses 410 12.2.1 Extending Regression using the Linear Mixed Model 410 12.2.2 Testing and Inference 414 12.2.3 Comparing Models 417 12.2.4 Special Cases: Random Block Designs and Multi‐level Sampling 418 12.3 Binary Responses 423 12.3.1 Extending Logistic Regression using Generalized Estimating Equations 423 12.3.2 Testing and Inference 425 12.4 Count Responses 427 12.4.1 Extending Poisson Regression using Generalized Estimating Equations 427 12.4.2 Testing and Inference 428 12.5 Computational Notes 431 Exercises 432 13 Analysis of Survival Data and Data from Matched Studies 439 13.1 Survival Data 440 13.2 Introductory Survival Analyses 443 13.2.1 Kaplan–Meier Curve 444 13.2.2 Comparison of Survival Distributions 446 13.3 Simple Regression and Correlation 450 13.3.1 Model and Approach 451 13.3.2 Measures of Association 452 13.3.3 Tests of Association 455 13.4 Multiple Regression and Correlation 456 13.4.1 Proportional Hazards Model with Several Covariates 456 13.4.2 Testing Hypotheses in Multiple Regression 457 13.4.3 Time‐Dependent Covariates and Applications 461 13.5 Pair‐Matched Case–Control Studies 464 13.5.1 Model 465 13.5.2 Analysis 466 13.6 Multiple Matching 468 13.6.1 Conditional Approach 469 13.6.2 Estimation of the Odds Ratio 469 13.6.3 Testing for Exposure Effect 470 13.7 Conditional Logistic Regression 472 13.7.1 Simple Regression Analysis 473 13.7.2 Multiple Regression Analysis 478 Exercises 484 14 Study Designs 493 14.1 Types of Study Designs 494 14.2 Classification of Clinical Trials 495 14.3 Designing Phase I Cancer Trials 497 14.4 Sample Size Determination for Phase II Trials and Surveys 499 14.5 Sample Sizes for Other Phase II Trials 501 14.5.1 Continuous Endpoints 501 14.5.2 Correlation Endpoints 502 14.6 About Simon’s Two‐Stage Phase II Design 503 14.7 Phase II Designs for Selection 504 14.7.1 Continuous Endpoints 505 14.7.2 Binary Endpoints 505 14.8 Toxicity Monitoring in Phase II Trials 506 14.9 Sample Size Determination for Phase III Trials 508 14.9.1 Comparison of Two Means 509 14.9.2 Comparison of Two Proportions 511 14.9.3 Survival Time as the Endpoint 513 14.10 Sample Size Determination for Case–Control Studies 515 14.10.1 Unmatched Designs for a Binary Exposure 516 14.10.2 Matched Designs for a Binary Exposure 518 14.10.3 Unmatched Designs for a Continuous Exposure 520 Exercises 522 References 529 Appendices 535 Answers to Selected Exercises 541 Index 585

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Book SynopsisA comprehensive and user-friendly introduction to statistics for behavioral science students?revised and updated Refined over seven editions by master teachers, this book gives instructors and students alike clear examples and carefully crafted exercises to support the teaching and learning of statistics for both manipulating and consuming data. One of the most popular and respected statistics texts in the behavioral sciences, the Seventh Edition of Introductory Statistics for the Behavioral Sciences has been fully revised. The new edition presents all the topics students in the behavioral sciences need in a uniquely accessible and easy-to-understand format, aiding in the comprehension and implementation of the statistical analyses most commonly used in the behavioral sciences. The Seventh Edition features: A continuous narrative that clearly explains statistics while tracking a common data set throughout, making the concepts unintimidating and Table of ContentsPreface xv Acknowledgments xix Glossary of Symbols xxi Part I Descriptive Statistics 1 Chapter 1 Introduction 3 Why Study Statistics? 4 Descriptive and Inferential Statistics 5 Populations, Samples, Parameters, and Statistics 6 Measurement Scales 7 Independent and Dependent Variables 10 Summation Notation 12 Ihno’s Study 16 Summary 18 Exercises 19 Thought Questions 23 Computer Exercises 23 Bridge to SPSS 24 Chapter 2 Frequency Distributions and Graphs 26 The Purpose of Descriptive Statistics 27 Regular Frequency Distributions 28 Cumulative Frequency Distributions 30 Grouped Frequency Distributions 31 Real and Apparent Limits 33 Interpreting a Raw Score 34 Definition of Percentile Rank and Percentile 34 Computational Procedures 35 Deciles, Quartiles, and the Median 38 Graphic Representations 39 Shapes of Frequency Distributions 43 Summary 45 Exercises 47 Thought Questions 49 Computer Exercises 49 Bridge to SPSS 50 Chapter 3 Measures of Central Tendency and Variability 53 Introduction 54 The Mode 56 The Median 56 The Mean 58 The Concept of Variability 62 The Range 65 The Standard Deviation and Variance 66 Summary 73 Exercises 75 Thought Questions 76 Computer Exercises 77 Bridge to SPSS 78 Chapter 4 Standardized Scores and the Normal Distribution 81 Interpreting a Raw Score Revisited 82 Rules for Changing μ and σ 84 Standard Scores (z Scores) 85 T Scores, SAT Scores, and IQ Scores 88 The Normal Distribution 90 Table of the Standard Normal Distribution 93 Illustrative Examples 95 Summary 101 Exercises 103 Thought Questions 105 Computer Exercises 106 Bridge to SPSS 106 Part II Basic Inferential Statistics 109 Chapter 5 Introduction to Statistical Inference 111 Introduction 113 The Goals of Inferential Statistics 114 Sampling Distributions 114 The Standard Error of the Mean 119 The z Score for Sample Means 122 Null Hypothesis Testing 124 Assumptions Required by the Statistical Test for the Mean of a Single Population 132 Summary 133 Exercises 135 Thought Questions 137 Computer Exercises 138 Bridge to SPSS 138 Appendix: The Null Hypothesis Testing Controversy 139 Chapter 6 The One-Sample t Test and Interval Estimation 142 Introduction 143 The Statistical Test for the Mean of a Single Population When σ Is Not Known: The t Distributions 144 Interval Estimation 148 The Standard Error of a Proportion 152 Summary 155 Exercises 156 Thought Questions 157 Computer Exercises 158 Bridge to SPSS 158 Chapter 7 Testing Hypotheses About the Difference Between the Means of Two Populations 160 The Standard Error of the Difference 162 Estimating the Standard Error of the Difference 166 The t Test for Two Sample Means 167 Confidence Intervals for μ1 − μ2 172 The Assumptions Underlying the Proper Use of the t Test for Two Sample Means 175 Measuring the Size of an Effect 176 The t Test for Matched Samples 178 Summary 185 Exercises 187 Thought Questions 190 Computer Exercises 191 Bridge to SPSS 191 Chapter 8 Nonparametric Tests for the Difference Between Two Means 194 Introduction 195 The Difference Between the Locations of Two Independent Samples: The Rank-Sum Test 199 The Difference Between the Locations of Two Matched Samples: The Wilcoxon Test 205 Summary 210 Exercises 212 Thought Questions 215 Computer Exercises 216 Bridge to SPSS 216 Chapter 9 Linear Correlation 218 Introduction 219 Describing the Linear Relationship Between Two Variables 222 Interpreting the Magnitude of a Pearson r 229 When Is It Important That Pearson’s r Be Large? 234 Testing the Significance of the Correlation Coefficient 236 The Relationship Between Two Ranked Variables: The Spearman Rank-Order Correlation Coefficient 239 Summary 242 Exercises 244 Thought Questions 247 Computer Exercises 248 Bridge to SPSS 248 Appendix: Equivalence of the Various Formulas for r 251 Chapter 10 Prediction and Linear Regression 253 Introduction 254 Using Linear Regression to Make Predictions 254 Measuring Prediction Error: The Standard Error of Estimate 263 The Connection Between Correlation and the t Test 265 Estimating the Proportion of Variance Accounted for in the Population 271 Summary 273 Exercises 275 Thought Questions 277 Computer Exercises 277 Bridge to SPSS 278 Chapter 11 Introduction to Power Analysis 281 Introduction 282 Concepts of Power Analysis 283 The Significance Test of the Mean of a Single Population 285 The Significance Test of the Proportion of a Single Population 290 The Significance Test of a Pearson r 292 Testing the Difference Between Independent Means 293 Testing the Difference Between the Means of Two Matched Populations 297 Choosing a Value for d for a Power Analysis Involving Independent Means 299 Using Power Analysis Concepts to Interpret the Results of Null Hypothesis Tests 301 Summary 304 Exercises 306 Thought Questions 308 Computer Exercises 309 Bridge to SPSS 310 Part III Analysis of Variance Methods 313 Chapter 12 One-Way Analysis of Variance 315 Introduction 317 The General Logic of ANOVA 318 Computational Procedures 321 Testing the F Ratio for Statistical Significance 326 Calculating the One-Way ANOVA From Means and Standard Deviations 328 Comparing the One-Way ANOVA With the t Test 329 A Simplified ANOVA Formula for Equal Sample Sizes 330 Effect Size for the One-Way ANOVA 331 Some Comments on the Use of ANOVA 333 A Nonparametric Alternative to the One-Way ANOVA: The Kruskal-Wallis H Test 336 Summary 339 Exercises 343 Thought Questions 346 Computer Exercises 346 Bridge to SPSS 346 Appendix: Proof That the Total Sum of Squares Is Equal to the Sum of the Between-Group and the Within-Group Sum of Squares 348 Chapter 13 Multiple Comparisons 349 Introduction 350 Fisher’s Protected t Tests and the Least Significant Difference (LSD) 351 Tukey’s Honestly Significant Difference (HSD) 355 Other Multiple Comparison Procedures 360 Planned and Complex Comparisons 362 Nonparametric Multiple Comparisons: The Protected Rank-Sum Test 365 Summary 366 Exercises 368 Thought Questions 369 Computer Exercises 370 Bridge to SPSS 370 Chapter 14 Introduction to Factorial Design: Two-Way Analysis of Variance 372 Introduction 373 Computational Procedures 374 The Meaning of Interaction 384 Following Up a Significant Interaction 387 Measuring Effect Size in a Factorial ANOVA 390 Summary 392 Exercises 395 Thought Questions 398 Computer Exercises 399 Bridge to SPSS 399 Chapter 15 Repeated-Measures ANOVA 402 Introduction 403 Calculating the One-Way RM ANOVA 403 Rationale for the RM ANOVA Error Term 408 Assumptions and Other Considerations Involving the RM ANOVA 408 The RM Versus RB Design: An Introduction to the Issues of Experimental Design 411 The Two-Way Mixed Design 415 Summary 423 Exercises 428 Thought Questions 430 Computer Exercises 430 Bridge to SPSS 431 Part IV Nonparametric Statistics for Categorical Data 435 Chapter 16 Probability of Discrete Events and the Binomial Distribution 437 Introduction 438 Probability 439 The Binomial Distribution 442 The Sign Test for Matched Samples 448 Summary 450 Exercises 451 Thought Questions 453 Computer Exercises 453 Bridge to SPSS 454 Chapter 17 Chi-Square Tests 457 Chi Square and the Goodness of Fit: One-Variable Problems 458 Chi Square as a Test of Independence: Two-Variable Problems 464 Measures of Strength of Association in Two-Variable Tables 470 Summary 472 Exercises 474 Thought Questions 476 Computer Exercises 477 Bridge to SPSS 478 Appendix 481 Statistical Tables 483 Answers to Odd-Numbered Exercises 499 Data From Ihno’s Experiment 511 Glossary of Terms 515 References 525 Index 527

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Book SynopsisTime Series Analysis in Meteorology and Climatology provides an accessible overview of this notoriously difficult subject. Clearly structured throughout, the authors develop sufficient theoretical foundation to understand the basis for applying various analytical methods to a time series and show clearly how to interpret the results.Trade Review“In summary, I unequivocally endorse this book as a valuable contribution to the literature of time series analysis in the geosciences. It is clear and includes examples that make it accessible for students; knowledgeable practitioners will also gain new insights from this book.” (Bulletin of the American Meteorological Society, 1 September 2012) Table of ContentsSeries foreword vii Preface ix 1. Fourier analysis 1 1.1 Overview and terminology 2 1.2 Analysis and synthesis 6 1.3 Example data sets 14 1.4 Statistical properties of the periodogram 23 1.5 Further important topics in Fourier analysis 47 Appendix 1.A Subroutine foranx 83 Appendix 1.B Sum of complex exponentials 86 Appendix 1.C Distribution of harmonic variances 86 Appendix 1.D Derivation of Equation 1.42 92 Problems 93 References 99 2. Linear systems 101 2.1 Input–output relationships 102 2.2 Evaluation of the convolution integral 104 2.3 Fourier transforms for analog data 110 2.4 The delta function 113 2.5 Special input functions 118 2.6 The frequency response function 122 2.7 Fourier transform of the convolution integral 128 2.8 Linear systems in series 130 2.9 Ideal interpolation formula 132 Problems 137 References 142 3. Filtering data 143 3.1 Recursive and nonrecursive filtering 144 3.2 Commonly used digital nonrecursive filters 150 3.3 Filter design 159 3.4 Lanczos filtering 161 Appendix 3.A Convolution of two running mean filters 173 Appendix 3.B Derivation of Equation 3.20 176 Appendix 3.C Subroutine sigma 177 Problems 180 References 182 4. Autocorrelation 183 4.1 Definition and properties 184 4.2 Formulas for the acvf and acf 188 4.3 The acvf and acf for stationary digital processes 192 4.4 The acvf and acf for selected processes 195 4.5 Statistical formulas 201 4.6 Confidence limits for the population mean 206 4.7 Variance of the acvf and acf estimators 211 Appendix 4.A Generating a normal random variable 215 Problems 216 References 221 5. Lagged-product spectrum analysis 223 5.1 The variance density spectrum 223 5.2 Relationship between the variance density spectrum and the acvf 226 5.3 Spectra of random processes 230 5.4 Spectra of selected processes 232 5.5 Smoothing the spectrum 236 Appendix 5.A Proof of Equation 5.11 239 Appendix 5.B Proof of Equation 5.12 240 Problems 241 References 243 Index 245

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Book SynopsisWhether you have only a distant recollection of high school algebra or use differential equations every day, this book offers examples of the impact of chance that will amuse and astonish.Trade ReviewAll 140 pages of What Are the Chances? are enjoyable and convey much wisdom in an area where gut feelings and rash actions frequently prevail. -- Colin Keay The Physicist An extremely fun read... Insightful and full of interesting applications. Chance Holland captures the reader's imagination with surprising examples of probability in action, everyday events that can profoundly affect our lives. It will amuse and astonish the reader. Journal of Irreproducible Results Holland Captures the reader's imagination with surprising examples of probability in action, everyday events that can profoundly affect our lives but are controlled by just one number. Mathematical Reviews What Are the Chances? is an enjoyable read. And painlessly instructive as well... [a] charming book. -- James Gerrand The Skeptic What Are the Chances? will give you a whole new outlook... readable, comprehendable, and often funny. -- Marilis Hornidge The Courier-Gazette If you have ever wondered about the chances of a Prussian cavalryman being kicked to death by his horse or if you prefer to work out your own life expectancy by staring at life tables, then Bart Holland's excellent primer on probability is a great place to start. In a time when anecdote and panic seem to influence public policy more than objective analysis, Holland has provided a welcome reminder of the power of the analytical approach. -- Simon Singh New Scientist Will entertain and inform people who like statistical puzzles and may nudge those who don't toward statistical literacy... Offers explanations of such probability-based phenomena as why buses come in clumps, how life insurance table work, and how diseases spread. While maintaining a sense of fun, Holland still manages to work in some equations and a little of the history behind different kinds of statistical reasoning. Library Journal Written to make minimal (almost zero) use of formulas or algebraic skills. Covers a remarkable number of topics [which are] introduced to stimulate the interest of the average reader. American Mathematical Monthly This is a book I can happily recommend... I learnt something from every chapter. -- Quentin L. Burrell Significance 2004 The author writes fluently and with authority and he covers a host of different situations... The strength of this book is the wealth of examples of applied probability theory which will provide useful support for any statistics course in the classroom. -- Gerry Leversha Mathematical Gazette 2004 An excellent source of interesting examples of probability and statistics in action. -- James V. Rauff Mathematics and Computer Education 2004Table of ContentsPrefaceAcknowledgmentsChapter 1. Roulette Wheels and the PlagueChapter 2. Surely Something's Wrong With YouChapter 3. The Life Table: You Can Bet On It!Chapter 4. The Rarest EventsChapter 5. The Waiting GameChapter 6. Stockbrokers and Climate ChangeIndex

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Book SynopsisStatistics help us create Internet technologies, develop medicines, win elections, invest in stocks, predict the weather, and more. But the methods that produce important numbers remain beyond many of us. This book take us on a tour of this subject. It explores the key foundational concepts of statistics and the perils of improper methods.

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Book SynopsisPraise for the First Edition extremely well writtena comprehensive and up-to-date overview of this important field. Journal of Environmental Quality Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition provides comprehensive coverage of recent advancements in microarray data analysis. A cutting-edge guide, the Second Edition demonstrates various methodologies for analyzing data in biomedical research and offers an overview of the modern techniques used in microarray technology to study patterns of gene activity. The new edition answers the need for an efficient outline of all phases of this revolutionary analytical technique, from preprocessing to the analysis stage. Utilizing research and experience from highly-qualified authors in fields of data analysis, Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition featurTrade Review“Featuring new information on interpretation of findings, class prediction, ABC clustering, limma for mixed models, biclustering, mass spectrometry, tracking Spearman correlations, and more, this \extremely well written" (Journal of Environmental Quality) book is a choice reference for scientists, teachers, and students interested in DNA data analysis.” (Zentralblatt MATH, 1 October 2014) “In summary this is an excellent text for both life scientist and computer/mathematicians. Highly recommended.” (Scientific Computing, 1 August 2014) Table of ContentsPreface xv Acknowledgments xvii 1 A brief introduction 1 1.1 A note on exploratory data analysis 3 1.2 Computing considerations and software 4 1.3 A brief outline of the book 5 1.4 Datasets and case studies 7 2 Genomics basics 11 2.1 Genes 11 2.2 DNA 12 2.3 Gene expression 13 2.4 Hybridization assays and other laboratory techniques 15 2.5 The human genome 16 2.6 Genome variations and their consequences 18 2.7 Genomics 19 2.8 The role of genomics in pharmaceutical and research and clinical practice 20 2.9 Proteins 23 2.10 Bioinformatics 23 3 Microarrays 27 3.1 Types of microarray experiments 28 3.2 A very simple hypothetical microarray experiment 32 3.3 A typical microarray experiment 34 3.4 Multichannel cDNA microarrays 38 3.5 Oligonucleotide microarrays 38 3.6 Bead based arrays 40 3.7 Confirmation of microarray results 40 4 Processing the scanned image 43 4.1 Converting the scanned image to the spotted image 44 4.2 Quality assessment 47 4.3 Adjusting for background 53 4.4 Expression level calculation for twochannel cDNA microarrays 56 4.5 Expression level calculation for oligonucleotide microarrays 58 5 Preprocessing microarray data 65 5.1 Logarithmic transformation 66 5.2 Variance stabilizing transformations 66 5.3 Sources of bias 68 5.4 Normalization 69 5.5 Intensity dependent normalization 70 5.6 Judging the success of a normalization 81 5.7 Outlier identification 83 5.8 Nonresistant rules for outlier identification 83 5.9 Resistant rules for outlier identification 83 5.10 Assessing replicate array quality 84 6 Summarization 95 6.1 Replication 95 6.2 Technical replicates 96 6.3 Biological replicates 100 6.4 Biological replicates 100 6.5 Multiple oligonucleotide arrays 102 6.6 Estimating fold change in twochannel experiments 104 6.7 Bayes estimation of fold change 105 6.8 Estimating fold change Affymetrix data 106 6.9 RMA Summarization of multiple oligonucleotide arrays revisited 107 6.10 FARMS summarization. 108 7 Two group comparative experiments 119 7.1 Basics of statistical hypothesis testing 120 7.2 Fold changes 123 7.3 The two sample t test 123 7.4 Diagnostic checks 127 7.5 Robust t tests 129 7.6 The Mann Whitney Wilcox on rank sum test 130 7.7 Multiplicity 132 7.8 The false discovery rate 135 7.9 Resampling based Multiple Testing Procedures 138 7.10 Small variance adjusted t tests and SAM 140 7.11 Conditional t 146 7.12 Borrowing strength across genes 149 7.13 Twochannel experiments 151 7.14 Filtering 153 8 Model based inference and experimental design considerations 177 8.1 The F test 178 8.2 The basic linear model 179 8.3 Fitting the model in two stages 181 8.4 Multichannel experiments 182 8.5 Experimental design considerations 183 8.6 Miscellaneous issues 187 8.7 Model based analysis of Affymetrix arrays 188 9 Analysis of gene sets 211 9.1 Methods for identifying enriched gene sets 213 9.2 ORA and Fisher’s exact test 217 9.3 Interpretation of results 217 9.4 Example 217 10 Pattern discovery 221 10.1 Initial considerations 222 10.2 Cluster analysis 223 10.3 Seeking patterns visually 241 10.4 Biclustering 254 11 Class prediction 263 11.1 Initial considerations 264 11.2 Linear Discriminant Analysis 269 11.3 Extensions of Fisher’s LDA 275 11.4 Penalized methods 278 11.5 Nearest neighbors 279 11.6 Recursive partitioning 280 11.7 Ensemble methods 285 11.8 Enriched ensemble classifiers 288 11.9 Neural networks 288 11.10 Support Vector Machines 289 11.11 Generalized enriched methods 291 11.12 Integration of genome information 301 12 Protein arrays 307 12.1 Introduction 307 12.2 Protein array experiments 308 12.3 Special issues with protein arrays 310 12.4 Analysis 310 12.5 Using antibody antigen arrays to measure protein concentrations 311 References 317 Index 337

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Book SynopsisA comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about conTrade Review"The exposition is quite clear, intuitive, and is a useful complement to more abstract treatises on stochastic calculus and simulation." (MathSciNet, 1 December 2015) “Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course.” (Zentralblatt MATH, 1 March 2014) “Statistical computing in its broadest sense is an ever-growing field far too extensive to be covered in a single text. The current book has a far more manageable scope, notwithstanding its title. Its focus is on the use of Monte Carlo methods to simulate random systems and explore statistical models.” (Mathematical Association of America, 1 January 2014) Table of ContentsList of algorithms ix Preface xi Nomenclature xiii 1 Random number generation 1 1.1 Pseudo random number generators 2 1.1.1 The linear congruential generator 2 1.1.2 Quality of pseudo random number generators 4 1.1.3 Pseudo random number generators in practice 8 1.2 Discrete distributions 8 1.3 The inverse transform method 11 1.4 Rejection sampling 15 1.4.1 Basic rejection sampling 15 1.4.2 Envelope rejection sampling 18 1.4.3 Conditional distributions 22 1.4.4 Geometric interpretation 26 1.5 Transformation of random variables 30 1.6 Special-purpose methods 36 1.7 Summary and further reading 36 Exercises 37 2 Simulating statistical models 41 2.1 Multivariate normal distributions 41 2.2 Hierarchical models 45 2.3 Markov chains 50 2.3.1 Discrete state space 51 2.3.2 Continuous state space 56 2.4 Poisson processes 58 2.5 Summary and further reading 67 Exercises 67 3 Monte Carlo methods 69 3.1 Studying models via simulation 69 3.2 Monte Carlo estimates 74 3.2.1 Computing Monte Carlo estimates 75 3.2.2 Monte Carlo error 76 3.2.3 Choice of sample size 80 3.2.4 Refined error bounds 82 3.3 Variance reduction methods 84 3.3.1 Importance sampling 84 3.3.2 Antithetic variables 88 3.3.3 Control variates 93 3.4 Applications to statistical inference 96 3.4.1 Point estimators 97 3.4.2 Confidence intervals 100 3.4.3 Hypothesis tests 103 3.5 Summary and further reading 106 Exercises 106 4 Markov Chain Monte Carlo methods 109 4.1 The Metropolis–Hastings method 110 4.1.1 Continuous state space 110 4.1.2 Discrete state space 113 4.1.3 Random walk Metropolis sampling 116 4.1.4 The independence sampler 119 4.1.5 Metropolis–Hastings with different move types 120 4.2 Convergence of Markov Chain Monte Carlo methods 125 4.2.1 Theoretical results 125 4.2.2 Practical considerations 129 4.3 Applications to Bayesian inference 137 4.4 The Gibbs sampler 141 4.4.1 Description of the method 141 4.4.2 Application to parameter estimation 146 4.4.3 Applications to image processing 151 4.5 Reversible Jump Markov Chain Monte Carlo 158 4.5.1 Description of the method 160 4.5.2 Bayesian inference for mixture distributions 171 4.6 Summary and further reading 178 4.6 Exercises 178 5 Beyond Monte Carlo 181 5.1 Approximate Bayesian Computation 181 5.1.1 Basic Approximate Bayesian Computation 182 5.1.2 Approximate Bayesian Computation with regression 188 5.2 Resampling methods 192 5.2.1 Bootstrap estimates 192 5.2.2 Applications to statistical inference 197 5.3 Summary and further reading 209 Exercises 209 6 Continuous-time models 213 6.1 Time discretisation 213 6.2 Brownian motion 214 6.2.1 Properties 216 6.2.2 Direct simulation 217 6.2.3 Interpolation and Brownian bridges 218 6.3 Geometric Brownian motion 221 6.4 Stochastic differential equations 224 6.4.1 Introduction 224 6.4.2 Stochastic analysis 226 6.4.3 Discretisation schemes 231 6.4.4 Discretisation error 236 6.5 Monte Carlo estimates 243 6.5.1 Basic Monte Carlo 243 6.5.2 Variance reduction methods 247 6.5.3 Multilevel Monte Carlo estimates 250 6.6 Application to option pricing 255 6.7 Summary and further reading 259 Exercises 260 Appendix A Probability reminders 263 A.1 Events and probability 263 A.2 Conditional probability 266 A.3 Expectation 268 A.4 Limit theorems 269 A.5 Further reading 270 Appendix B Programming in R 271 B.1 General advice 271 B.2 R as a Calculator 272 B.2.1 Mathematical operations 273 B.2.2 Variables 273 B.2.3 Data types 275 B.3 Programming principles 282 B.3.1 Don’t repeat yourself! 283 B.3.2 Divide and conquer! 286 B.3.3 Test your code! 290 B.4 Random number generation 292 B.5 Summary and further reading 294 Exercises 294 Appendix C Answers to the exercises 299 C.1 Answers for Chapter 1 299 C.2 Answers for Chapter 2 315 C.3 Answers for Chapter 3 319 C.4 Answers for Chapter 4 328 C.5 Answers for Chapter 5 342 C.6 Answers for Chapter 6 350 C.7 Answers for Appendix B 366 References 375 Index 379

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Book SynopsisThis complete resource on the theory and applications of reliability engineering, probabilistic models and risk analysis consolidates all the latest research, presenting the most up-to-date developments in this field.Table of ContentsRemembering Boris Gnedenko xvii List of Contributors xxv Preface xxix Acknowledgements xxxv Part I DEGRADATION ANALYSIS, MULTI-STATE AND CONTINUOUS-STATE SYSTEM RELIABILITY 1 Methods of Solutions of Inhomogeneous Continuous Time Markov Chains for Degradation Process Modeling 3 Yan-Fu Li, Enrico Zio and Yan-Hui Lin 1.1 Introduction 3 1.2 Formalism of ICTMC 4 1.3 Numerical Solution Techniques 5 1.4 Examples 10 1.5 Comparisons of the Methods and Guidelines of Utilization 13 1.6 Conclusion 15 References 15 2 Multistate Degradation and Condition Monitoring for Devices with Multiple Independent Failure Modes 17 Ramin Moghaddass and Ming J. Zuo 2.1 Introduction 17 2.2 Multistate Degradation and Multiple Independent Failure Modes 19 2.3 Parameter Estimation 23 2.4 Important Reliability Measures of a Condition-Monitored Device 25 2.5 Numerical Example 27 2.6 Conclusion 28 Acknowledgements 30 References 30 3 Time Series Regression with Exponential Errors for Accelerated Testing and Degradation Tracking 32 Nozer D. Singpurwalla 3.1 Introduction 32 3.2 Preliminaries: Statement of the Problem 33 3.3 Estimation and Prediction by Least Squares 34 3.4 Estimation and Prediction by MLE 35 3.5 The Bayesian Approach: The Predictive Distribution 37 Acknowledgements 42 References 42 4 Inverse Lz-Transform for a Discrete-State Continuous-Time Markov Process and Its Application to Multi-State System Reliability Analysis 43 Anatoly Lisnianski and Yi Ding 4.1 Introduction 43 4.2 Inverse Lz-Transform: Definitions and Computational Procedure 44 4.3 Application of Inverse Lz-Transform to MSS Reliability Analysis 50 4.4 Numerical Example 52 4.5 Conclusion 57 References 58 5 OntheLz-Transform Application for Availability Assessment of an Aging Multi-State Water Cooling System for Medical Equipment 59 Ilia Frenkel, Anatoly Lisnianski and Lev Khvatskin 5.1 Introduction 59 5.2 Brief Description of the Lz-Transform Method 61 5.3 Multi-state Model of the Water Cooling System for the MRI Equipment 62 5.4 Availability Calculation 75 5.5 Conclusion 76 Acknowledgments 76 References 77 6 Combined Clustering and Lz-Transform Technique to Reduce the Computational Complexity of a Multi-State System Reliability Evaluation 78 Yi Ding 6.1 Introduction 78 6.2 The Lz-Transform for Dynamic Reliability Evaluation for MSS 79 6.3 Clustering Composition Operator in the Lz-Transform 81 6.4 Computational Procedures 83 6.5 Numerical Example 83 6.6 Conclusion 85 References 85 7 Sliding Window Systems with Gaps 87 Gregory Levitin 7.1 Introduction 87 7.2 The Models 89 7.3 Reliability Evaluation Technique 91 7.4 Conclusion 96 References 96 8 Development of Reliability Measures Motivated by Fuzzy Sets for Systems with Multi- or Infinite-States 98 Zhaojun (Steven) Li and Kailash C. Kapur 8.1 Introduction 98 8.2 Models for Components and Systems Using Fuzzy Sets 100 8.3 Fuzzy Reliability for Systems with Continuous or Infinite States 103 8.4 Dynamic Fuzzy Reliability 104 8.5 System Fuzzy Reliability 110 8.6 Examples and Applications 111 8.7 Conclusion 117 References 118 9 Imperatives for Performability Design in the Twenty-First Century 119 Krishna B. Misra 9.1 Introduction 119 9.2 Strategies for Sustainable Development 120 9.3 Reappraisal of the Performance of Products and Systems 124 9.4 Dependability and Environmental Risk are Interdependent 126 9.5 Performability: An Appropriate Measure of Performance 126 9.6 Towards Dependable and Sustainable Designs 129 9.7 Conclusion 130 References 130 Part II NETWORKS AND LARGE-SCALE SYSTEMS 10 Network Reliability Calculations Based on Structural Invariants 135 Ilya B. Gertsbakh and Yoseph Shpungin 10.1 First Invariant: D-Spectrum, Signature 135 10.2 Second Invariant: Importance Spectrum. Birnbaum Importance Measure (BIM) 139 10.3 Example: Reliability of a Road Network 141 10.4 Third Invariant: Border States 142 10.5 Monte Carlo to Approximate the Invariants 144 10.6 Conclusion 146 References 146 11 Performance and Availability Evaluation of IMS-Based Core Networks 148 Kishor S. Trivedi, Fabio Postiglione and Xiaoyan Yin 11.1 Introduction 148 11.2 IMS-Based Core Network Description 149 11.3 Analytic Models for Independent Software Recovery 151 11.4 Analytic Models for Recovery with Dependencies 155 11.5 Redundancy Optimization 158 11.6 Numerical Results 159 11.7 Conclusion 165 References 165 12 Reliability and Probability of First Occurred Failure for Discrete-Time Semi-Markov Systems 167 Stylianos Georgiadis, Nikolaos Limnios and Irene Votsi 12.1 Introduction 167 12.2 Discrete-Time Semi-Markov Model 168 12.3 Reliability and Probability of First Occurred Failure 170 12.4 Nonparametric Estimation of Reliability Measures 172 12.5 Numerical Application 176 12.6 Conclusion 178 References 179 13 Single-Source Epidemic Process in a System of Two Interconnected Networks 180 Ilya B. Gertsbakh and Yoseph Shpungin 13.1 Introduction 180 13.2 Failure Process and the Distribution of the Number of Failed Nodes 181 13.3 Network Failure Probabilities 184 13.4 Example 185 13.5 Conclusion 187 13.A Appendix D: Spectrum (Signature) 188 References 189 Part III MAINTENANCE MODELS 14 Comparisons of Periodic and Random Replacement Policies 193 Xufeng Zhao and Toshio Nakagawa 14.1 Introduction 193 14.2 Four Policies 195 14.3 Comparisons of Optimal Policies 197 14.4 Numerical Examples 1 199 14.5 Comparisons of Policies with Different Replacement Costs 201 14.6 Numerical Examples 2 202 14.7 Conclusion 203 Acknowledgements 204 References 204 15 Random Evolution of Degradation and Occurrences of Words in Random Sequences of Letters 205 Emilio De Santis and Fabio Spizzichino 15.1 Introduction 205 15.2 Waiting Times to Words’ Occurrences 206 15.3 Some Reliability-Maintenance Models 209 15.4 Waiting Times to Occurrences of Words and Stochastic Comparisons for Degradation 213 15.5 Conclusions 216 Acknowledgements 217 References 217 16 Occupancy Times for Markov and Semi-Markov Models in Systems Reliability 218 Alan G. Hawkes, Lirong Cui and Shijia Du 16.1 Introduction 218 16.2 Markov Models for Systems Reliability 220 16.3 Semi-Markov Models 222 16.4 Time Interval Omission 225 16.5 Numerical Examples 226 16.6 Conclusion 229 Acknowledgements 229 References 229 17 A Practice of Imperfect Maintenance Model Selection for Diesel Engines 231 Yu Liu, Hong-Zhong Huang, Shun-Peng Zhu and Yan-Feng Li 17.1 Introduction 231 17.2 Review of Imperfect Maintenance Model Selection Method 233 17.3 Application to Preventive Maintenance Scheduling of Diesel Engines 236 17.4 Conclusion 244 Acknowledgment 245 References 245 18 Reliability of Warm Standby Systems with Imperfect Fault Coverage 246 Rui Peng, Ola Tannous, Liudong Xing and Min Xie 18.1 Introduction 246 18.2 Literature Review 247 18.3 The BDD-Based Approach 250 18.4 Conclusion 253 Acknowledgments 254 References 254 Part IV STATISTICAL INFERENCE IN RELIABILITY 19 On the Validity of the Weibull-Gnedenko Model 259 Vilijandas Bagdonavi¡cius, Mikhail Nikulin and Ruta Levuliene 19.1 Introduction 259 19.2 Integrated Likelihood Ratio Test 261 19.3 Tests based on the Difference of Non-Parametric and Parametric Estimators of the Cumulative Distribution Function 264 19.4 Tests based on Spacings 266 19.5 Chi-Squared Tests 267 19.6 Correlation Test 269 19.7 Power Comparison 269 19.8 Conclusion 272 References 272 20 Statistical Inference for Heavy-Tailed Distributions in Reliability Systems 273 Ilia Vonta and Alex Karagrigoriou 20.1 Introduction 273 20.2 Heavy-Tailed Distributions 274 20.3 Examples of Heavy-Tailed Distributions 277 20.4 Divergence Measures 280 20.5 Hypothesis Testing 284 20.6 Simulations 286 20.7 Conclusion 287 References 287 21 Robust Inference based on Divergences in Reliability Systems 290 Abhik Ghosh, Avijit Maji and Ayanendranath Basu 21.1 Introduction 290 21.2 The Power Divergence (PD) Family 291 21.3 Density Power Divergence (DPD) and Parametric Inference 296 21.4 A Generalized Form: The S-Divergence 301 21.5 Applications 304 21.6 Conclusion 306 References 306 22 COM-Poisson Cure Rate Models and Associated Likelihood-based Inference with Exponential and Weibull Lifetimes 308 N. Balakrishnan and Suvra Pal 22.1 Introduction 308 22.2 Role of Cure Rate Models in Reliability 310 22.3 The COM-Poisson Cure Rate Model 310 22.4 Data and the Likelihood 311 22.5 EM Algorithm 312 22.6 Standard Errors and Asymptotic Confidence Intervals 314 22.7 Exponential Lifetime Distribution 314 22.8 Weibull Lifetime Distribution 322 22.9 Analysis of Cutaneous Melanoma Data 334 22.10 Conclusion 337 22.A1 Appendix A1: E-Step and M-Step Formulas for Exponential Lifetimes 337 22.A2 Appendix A2: E-Step and M-Step Formulas for Weibull Lifetimes 341 22.B1 Appendix B1: Observed Information Matrix for Exponential Lifetimes 344 22.B2 Appendix B2: Observed Information Matrix for Weibull Lifetimes 346 References 347 23 Exponential Expansions for Perturbed Discrete Time Renewal Equations 349 Dmitrii Silvestrov and Mikael Petersson 23.1 Introduction 349 23.2 Asymptotic Results 350 23.3 Proofs 353 23.4 Discrete Time Regenerative Processes 358 23.5 Queuing and Risk Applications 359 References 361 24 On Generalized Extreme Shock Models under Renewal Shock Processes 363 Ji Hwan Cha and Maxim Finkelstein 24.1 Introduction 363 24.2 Generalized Extreme Shock Models 364 24.3 Specific Models 367 24.4 Conclusion 373 Acknowledgements 373 References 373 Part V SYSTEMABILITY, PHYSICS-OF-FAILURE AND RELIABILITY DEMONSTRATION 25 Systemability Theory and its Applications 377 Hoang Pham 25.1 Introduction 377 25.2 Systemability Measures 378 25.3 Systemability Analysis of k-out-of-n Systems 379 25.4 Systemability Function Approximation 380 25.5 Systemability with Loglog Distribution 383 25.6 Sensitivity Analysis 384 25.7 Applications: Red Light Camera Systems 385 25.8 Conclusion 387 References 387 26 Physics-of-Failure based Reliability Engineering 389 Pedro O. Quintero and Michael Pecht 26.1 Introduction 389 26.2 Physics-of-Failure-based Reliability Assessment 393 26.3 Uses of Physics-of-Failure 398 26.4 Conclusion 400 References 400 27 Accelerated Testing: Effect of Variance in Field Environmental Conditions on the Demonstrated Reliability 403 Andre Kleyner 27.1 Introduction 403 27.2 Accelerated Testing and Field Stress Variation 404 27.3 Case Study: Reliability Demonstration Using Temperature Cycling Test 405 27.4 Conclusion 408 References 408 Index 409

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Book SynopsisA guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions. Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes: Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk managementTopical discussions on univariate and multivariate case extremes as well as regulation in financial marketsExtensive references in order to provide readers with resources for further studyDiscussions on using R packages to compute the value of risk and related quantities The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance.Table of ContentsAbout the Editor xiii About the Contributors xv 1 Introduction 1François Longin 1.1 Extremes 1 1.2 History 2 1.3 Extreme value theory 2 1.4 Statistical estimation of extremes 2 1.5 Applications in finance 4 1.6 Practitioners’ points of view 6 1.7 A broader view on modeling extremes 6 1.8 Final words 7 1.9 Thank you note 7 References 8 2 Extremes Under Dependence—Historical Development and Parallels with Central Limit Theory 11M.R. Leadbetter 2.1 Introduction 11 2.2 Classical (I.I.D.) central limit and extreme value theories 12 2.3 Exceedances of levels, kth largest values 14 2.4 CLT and EVT for stationary sequences, bernstein’s blocks, and strong mixing 15 2.5 Weak distributional mixing for EVT, D(un), extremal index 18 2.6 Point process of level exceedances 19 2.7 Continuous parameter extremes 20 References 22 3 The Extreme Value Problem in Finance: Comparing the Pragmatic Program with the Mandelbrot Program 25Christian Walter 3.1 The extreme value puzzle in financial modeling 25 3.2 The sato classification and the two programs 28 3.3 Mandelbrot’s program: A fractal approach 34 3.4 The Pragmatic Program: A data-driven approach 39 3.5 Conclusion 47 Acknowledgments 48 References 48 4 Extreme Value Theory: An Introductory Overview 53Isabel Fraga Alves and Cláudia Neves 4.1 Introduction 53 4.2 Univariate case 56 4.3 Multivariate case: Some highlights 84 Further reading 90 Acknowledgments 90 References 90 5 Estimation of the Extreme Value Index 97Beirlant J., Herrmann K., and Teugels J.L. 5.1 Introduction 97 5.2 The main limit theorem behind extreme value theory 98 5.3 Characterizations of the max-domains of attraction and extreme value index estimators 99 5.4 Consistency and asymptotic normality of the estimators 103 5.5 Second-order reduced-bias estimation 104 5.6 Case study 106 5.7 Other topics and comments 108 References 111 6 Bootstrap Methods in Statistics of Extremes 117M. Ivette Gomes, Frederico Caeiro, Lígia Henriques-Rodrigues, and B.G. Manjunath 6.1 Introduction 117 6.2 A few details on EVT 119 6.3 The bootstrap methodology in statistics of univariate extremes 127 6.4 Applications to simulated data 133 6.5 Concluding remarks 133 Acknowledgments 135 References 135 7 Extreme Values Statistics for Markov Chains with Applications to Finance and Insurance 139Patrice Bertail, Stéphan Clémençon, and Charles Tillier 7.1 Introduction 139 7.2 On the (pseudo) regenerative approach for markovian data 141 7.3 Preliminary results 151 7.4 Regeneration-based statistical methods for extremal events 154 7.5 The extremal index 156 7.6 The regeneration-based hill estimator 159 7.7 Applications to ruin theory and financial time series 161 7.8 An application to the CAC40 165 7.9 Conclusion 167 References 167 8 Lévy Processes and Extreme Value Theory 171Olivier Le Courtois and Christian Walter 8.1 Introduction 171 8.2 Extreme value theory 173 8.3 Infinite divisibility and Lévy processes 178 8.4 Heavy-tailed Lévy processes 182 8.5 Semi-heavy-tailed Lévy processes 184 8.6 Lévy processes and extreme values 187 8.7 Conclusion 192 References 192 9 Statistics of Extremes: Challenges and Opportunities 195M. de Carvalho 9.1 Introduction 195 9.2 Statistics of bivariate extremes 196 9.3 Models based on families of tilted measures 204 9.4 Miscellanea 209 References 211 10 Measures of Financial Risk 215S.Y. Novak 10.1 Introduction 215 10.2 Traditional measures of risk 215 10.3 Risk estimation 218 10.4 “Technical analysis” of financial data 222 10.5 Dynamic risk measurement 226 10.6 Open problems and further research 234 10.7 Conclusion 235 Acknowledgment 235 References 235 11 On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures 239Marie Kratz 11.1 Introduction 239 11.2 A brief review of existing methods 245 11.3 New approaches: Mixed limit theorems 247 11.4 Application to risk measures and comparison 269 11.5 Conclusion 277 References 279 12 Estimation Methods for Value at Risk 283Saralees Nadarajah and Stephen Chan 12.1 Introduction 283 12.2 General properties 289 12.3 Parametric methods 300 12.4 Nonparametric methods 326 12.5 Semiparametric methods 332 12.6 Computer software 344 12.7 Conclusions 347 Acknowledgment 347 References 347 13 Comparing Tail Risk and Systemic Risk Profiles for Different Types of U.S. Financial Institutions 357Stefan Straetmans and Thanh Thi Huyen Dinh 13.1 Introduction 357 13.2 Tail risk and systemic risk indicators 361 13.3 Tail risk and systemic risk estimation 364 13.4 Empirical results 368 13.5 Conclusions 381 References 382 14 Extreme Value Theory and Credit Spreads 391Wesley Phoa 14.1 Preliminaries 391 14.2 Tail behavior of credit markets 394 14.3 Some multivariate analysis 398 14.4 Approximating value at risk for credit portfolios 401 14.5 Other directions 403 References 404 15 Extreme Value Theory and Risk Management in Electricity Markets 405Kam Fong Chan and Philip Gray 15.1 Introduction 405 15.2 Prior literature 407 15.3 Specification of VaR estimation approaches 409 15.4 Empirical analysis 413 15.5 Conclusion 422 Acknowledgment 423 References 423 16 Margin Setting and Extreme Value Theory 427John Cotter and Kevin Dowd 16.1 Introduction 427 16.2 Margin setting 428 16.3 Theory and methods 430 16.4 Empirical results 434 16.5 Conclusions 439 Acknowledgment 440 References 440 17 The Sortino Ratio and Extreme Value Theory: An Application to Asset Allocation 443G. Geoffrey Booth and John Paul Broussard 17.1 Introduction 443 17.2 Data definitions and description 446 17.3 Performance ratios and their estimations 451 17.4 Performance measurement results and implications 456 17.5 Concluding remarks 460 Acknowledgments 461 References 461 18 Portfolio Insurance: The Extreme Value Approach Applied to the CPPI Method 465Philippe Bertrand and Jean-Luc Prigent 18.1 Introduction 465 18.2 The CPPI method 467 18.3 CPPI and quantile hedging 472 18.4 Conclusion 481 References 481 19 The Choice of the Distribution of Asset Returns: How Extreme Value Can Help? 483François Longin 19.1 Introduction 483 19.2 Extreme value theory 485 19.3 Estimation of the tail index 488 19.4 Application of extreme value theory to discriminate among distributions of returns 490 19.5 Empirical results 493 19.6 Conclusion 501 References 501 20 Protecting Assets Under Non-Parametric Market Conditions 507Jean-Marie Choffray and Charles Pahud de Mortanges 20.1 Investors’ “known knowns” 509 20.2 Investors’ “known unknowns” 512 20.3 Investors’ “unknown knowns” 515 20.4 Investors’ “unknown unknowns” 518 20.5 Synthesis 522 References 523 21 EVT Seen by a Vet: A Practitioner’s Experience on Extreme Value Theory 525Jean-François Boulier 21.1 What has the vet done? 525 21.2 Why use EVT? 526 21.3 What EVT could additionally bring to the party? 528 21.4 A final thought 528 References 528 22 The Robotization of Financial Activities: A Cybernetic Perspective 529Hubert Rodarie 22.1 An increasingly complex system 530 22.2 Human error 532 22.3 Concretely, what do we need to do to transform a company into a machine? 534 References 543 23 Two Tales of Liquidity Stress 545Jacques Ninet 23.1 The french money market fund industry. How history has shaped a potentially vulnerable framework 546 23.2 The 1992–1995 forex crisis 547 23.3 Four mutations paving the way for another meltdown 549 23.4 The subprime crisis spillover. How some MMFs were forced to lock and some others not 551 23.5 Conclusion. What lessons can be drawn from these two tales? 552 Further Readings 553 24 Managing Operational Risk in the Banking Business – An Internal Auditor Point of View 555Maxime Laot Further Reading 559 References 560 Annexes 560 25 Credo Ut Intelligam 563Henri Bourguinat and Eric Briys 25.1 Introduction 563 25.2 “Anselmist” finance 563 25.3 Casino or dance hall? 565 25.4 Simple-minded diversification 566 25.5 Homo sapiens versus homo economicus 568 Acknowledgement 569 References 569 26 Bounded Rationalities, Routines, and Practical as well as Theoretical Blindness: On the Discrepancy Between Markets and Corporations 571Laurent Bibard 26.1 Introduction: Expecting the unexpected 571 26.2 Markets and corporations: A structural and self-disruptive divergence of interests 572 26.3 Making a step back from a dream: On people expectations 574 26.4 How to disentangle people from a unilateral short-term orientation? 578 References 580 Name Index 583 Subject Index 593

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Book SynopsisCategorical Statistics for CommunicationResearch presents scholars with a discipline-specific guide to categorical data analysis. The text blends necessary background information and formulas for statistical procedures with data analyses illustrating techniques such as log- linear modeling and logistic regression analysis.Table of ContentsDetailed Contents ix Preface xiii Acknowledgments xix About the Companion Website xx 1. Introduction to Categorical Statistics 1 2. Univariate Goodness of Fit and Contingency Tables in Two Dimensions 12 3. Contingency Tables in Three Dimensions 41 4. Log -linear Analysis 58 5. Logit Log -linear Analysis 90 6. Binary Logistic Regression 119 7. Multinomial Logistic Regression 153 8. Ordinal Logistic Regression 171 9. Probit Analysis 198 10. Poisson and Negative Binomial Regression 216 11. Interrater Agreement Measures for Nominal and Ordinal Data 232 12. Concluding Communication 255 Appendix A: Chi ]Square Table 259 Appendix B: SPSS Code for Selected Procedures 261 Index 266

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Book SynopsisA key resource and framework for assessing the performance of competing entities, including forecasting models Advances in DEA Theory and Applications provides a much-needed framework for assessing the performance of competing entities with special emphasis on forecasting models. It helps readers to determine the most appropriate methodology in order to make the most accurate decisions for implementation. Written by a noted expert in the field, this text provides a review of the latest advances in DEA theory and applications to the field of forecasting. Designed for use by anyone involved in research in the field of forecasting or in another application area where forecasting drives decision making, this text can be applied to a wide range of contexts, including education, health care, banking, armed forces, auditing, market research, retail outlets, organizational effectiveness, transportation, public housing, and manufacturing. This vital resource: Table of ContentsLIST OF CONTRIBUTORS xx ABOUT THE AUTHORS xxii PREFACE xxxii PART I DEA THEORY 1 1 Radial DEA Models 3Kaoru Tone 1.1 Introduction 3 1.2 Basic Data 3 1.3 Input-Oriented CCR Model 4 1.4 The Input-Oriented BCC Model 6 1.5 The Output-Oriented Model 7 1.6 Assurance Region Method 8 1.7 The Assumptions Behind Radial Models 8 1.8 A Sample Radial Model 8 References 10 2 Non-Radial DEA Models 11Kaoru Tone 2.1 Introduction 11 2.2 The SBM Model 12 2.3 An Example of an SBM Model 15 2.4 The Dual Program of the SBM Model 17 2.5 Extensions of the SBM Model 17 2.6 Concluding Remarks 18 References 19 3 Directional Distance DEA Models 20Hirofumi Fukuyama and William L. Weber 3.1 Introduction 20 3.2 Directional Distance Model 20 3.3 Variable-Returns-to-Scale DD Models 23 3.4 Slacks-Based DD Model 23 3.5 Choice of Directional Vectors 25 References 26 4 Super-Efficiency DEA Models 28Kaoru Tone 4.1 Introduction 28 4.2 Radial Super-Efficiency Models 28 4.3 Non-Radial Super-Efficiency Models 29 4.4 An Example of a Super-Efficiency Model 31 References 32 5 Determining Returns to Scale in the VRS DEA Model 33Biresh K. Sahoo and Kaoru Tone 5.1 Introduction 33 5.2 Technology Specification and Scale Elasticity 34 5.3 Summary 37 References 37 6 Malmquist Productivity Index Models 40Kaoru Tone and Miki Tsutsui 6.1 Introduction 40 6.2 Radial Malmquist Model 43 6.3 Non-Radial and Oriented Malmquist Model 45 6.4 Non-Radial and Non-Oriented Malmquist Model 47 6.5 Cumulative Malmquist Index (CMI) 48 6.6 Adjusted Malmquist Index (AMI) 49 6.7 Numerical Example 50 6.8 Concluding Remarks 55 References 55 7 The Network DEA Model 57Kaoru Tone and Miki Tsutsui 7.1 Introduction 57 7.2 Notation and Production Possibility Set 58 7.3 Description of Network Structure 59 7.4 Objective Functions and Efficiencies 61 Reference 63 8 The Dynamic DEA Model 64Kaoru Tone and Miki Tsutsui 8.1 Introduction 64 8.2 Notation and Production Possibility Set 65 8.3 Description of Dynamic Structure 67 8.4 Objective Functions and Efficiencies 69 8.5 Dynamic Malmquist Index 71 References 73 9 The Dynamic Network DEA Model 74Kaoru Tone and Miki Tsutsui 9.1 Introduction 74 9.2 Notation and Production Possibility Set 75 9.3 Description of Dynamic Network Structure 77 9.4 Objective Function and Efficiencies 80 9.5 Dynamic Divisional Malmquist Index 82 References 84 10 Stochastic DEA: The Regression-Based Approach 85Andrew L. Johnson 10.1 Introduction 85 10.2 Review of Literature on Stochastic DEA 87 10.3 Conclusions 96 References 96 11 A Comparative Study of AHP and DEA 100Kaoru Tone 11.1 Introduction 100 11.2 A Glimpse of Data Envelopment Analysis 100 11.3 Benefit/Cost Analysis by Analytic Hierarchy Process 102 11.4 Efficiencies in AHP and DEA 104 11.5 Concluding Remarks 105 References 106 12 A Computational Method for Solving DEA Problems with Infinitely Many DMUs 107Abraham Charnes and Kaoru Tone 12.1 Introduction 107 12.2 Problem 108 12.3 Outline of the Method 109 12.4 Details of the Method When Z is One-Dimensional 110 12.5 General Case 113 12.6 Concluding Remarks (by Tone) 115 Appendix 12.A Proof of Theorem 12.1 115 Appendix 12.B Proof of Theorem 12.2 116 Reference 116 PART II DEA APPLICATIONS (PAST–PRESENT SCENARIO) 117 13 Examining the Productive Performance of Life Insurance Corporation of India 119Kaoru Tone and Biresh K. Sahoo 13.1 Introduction 119 13.2 Nonparametric Approach to Measuring Scale Elasticity 121 13.3 The Dataset for LIC Operations 128 13.4 Results and Discussion 130 13.5 Concluding Remarks 136 References 136 14 An Account of DEA-Based Contributions in the Banking Sector 141Jamal Ouenniche, Skarleth Carrales, Kaoru Tone and Hirofumi Fukuyama 14.1 Introduction 141 14.2 Performance Evaluation of Banks: A Detailed Account 142 14.3 Current State of the Art Summarized 154 14.4 Conclusion 163 References 169 15 DEA in the Healthcare Sector 172Hiroyuki Kawaguchi, Kaoru Tone and Miki Tsutsui 15.1 Introduction 172 15.2 Method and Data 174 15.3 Results 184 15.4 Discussion 188 Acknowledgements 189 References 190 16 DEA in the Transport Sector 192Ming-Miin Yu and Li-Hsueh Chen 16.1 Introduction 192 16.2 DNDEA in Transport 194 16.3 Extension 200 16.4 Application 207 16.5 Conclusions 212 References 212 17 Dynamic Network Efficiency of Japanese Prefectures 216Hirofumi Fukuyama, Atsuo Hashimoto, Kaoru Tone and William L. Weber 17.1 Introduction 216 17.2 Multiperiod Dynamic Multiprocess Network 217 17.3 Efficiency/Productivity Measurement 221 17.4 Empirical Application 222 17.5 Conclusions 229 References 229 18 A Quantitative Analysis of Market Utilization in Electric Power Companies 231Miki Tsutsui and Kaoru Tone 18.1 Introduction 231 18.2 The Functions of the Trading Division 232 18.3 Measuring the Effect of Energy Trading 235 18.4 DEA Calculation 242 18.5 Empirical Results 243 18.6 Concluding Remarks 248 References 249 19 DEA in Resource Allocation 250Ming-Miin Yu and Li-Hsueh Chen 19.1 Introduction 250 19.2 Centralized DEA in Resource Allocation 252 19.3 Applications of Centralized DEA in Resource Allocation 261 19.4 Extension 265 19.5 Conclusions 268 References 268 20 How to Deal with Non-convex Frontiers in Data Envelopment Analysis 271Kaoru Tone and Miki Tsutsui 20.1 Introduction 271 20.2 Global Formulation 273 20.3 In-cluster Issue: Scale- and Cluster-Adjusted DEA Score 276 20.4 An Illustrative Example 281 20.5 The Radial-Model Case 284 20.6 Scale-Dependent Dataset and Scale Elasticity 287 20.7 Application to a Dataset Concerning Japanese National Universities 289 20.8 Conclusions 294 Appendix 20.A Clustering Using Returns to Scale and Scale Efficiency 295 Appendix 20.B Proofs of Propositions 295 References 298 21 Using DEA to Analyze the Efficiency of Welfare Offices and Influencing Factors: The Case of Japan’s Municipal Public Assistance Programs 300Masayoshi Hayashi 21.1 Introduction 300 21.2 Institutional Background, DEA, and Efficiency Scores 301 21.3 External Effects on Efficiency 304 21.4 Quantile Regression Analysis 309 21.5 Concluding Remarks 312 Acknowledgements 312 References 312 22 DEA as a Kaizen Tool: SBM Variations Revisited 315Kaoru Tone 22.1 Introduction 315 22.2 The SBM-Min Model 316 22.3 The SBM-Max Model 318 22.4 Observations 321 22.5 Numerical Examples 323 22.6 Conclusions 330 References 330 PART III DEA FOR FORECASTING AND DECISION-MAKING (PAST–PRESENT–FUTURE SCENARIO) 331 23 Corporate Failure Analysis Using SBM 333Joseph C. Paradi, Xiaopeng Yang and Kaoru Tone 23.1 Introduction 333 23.2 Literature Review 334 23.3 Methodology 340 23.4 Application to Bankruptcy Prediction 343 23.5 Conclusions 352 References 354 24 Ranking of Bankruptcy Prediction Models under Multiple Criteria 357Jamal Ouenniche, Mohammad M. Mousavi, Bing Xu and Kaoru Tone 24.1 Introduction 357 24.2 An Overview of Bankruptcy Prediction Models 359 24.3 A Slacks-Based Super-Efficiency Framework for Assessing Bankruptcy Prediction Models 366 24.4 Empirical Results from Super-Efficiency DEA 372 24.5 Conclusion 376 References 377 25 DEA in Performance Evaluation of Crude Oil Prediction Models 381Jamal Ouenniche, Bing Xu and Kaoru Tone 25.1 Introduction 381 25.2 An Overview of Crude Oil Prices and Their Volatilities 385 25.3 Assessment of Prediction Models of Crude Oil Price Volatility 388 25.4 Conclusion 401 References 402 26 Predictive Efficiency Analysis: A Study of US Hospitals 404Andrew L. Johnson and Chia-Yen Lee 26.1 Introduction 404 26.2 Modeling of Predictive Efficiency 405 26.3 Study of US Hospitals 408 26.4 Forecasting, Benchmarking, and Frontier Shifting 412 26.5 Conclusions 416 References 417 27 Efficiency Prediction Using Fuzzy Piecewise Autoregression 419Ming-Miin Yu and Bo Hsiao 27.1 Introduction 419 27.2 Efficiency Prediction 420 27.3 Modeling and Formulation 423 27.4 Illustrating the Application 433 27.5 Discussion 438 27.6 Conclusion 440 References 441 28 Time Series Benchmarking Analysis for New Product Scheduling: Who Are the Competitors and How Fast Are They Moving Forward? 443Dong-Joon Lim and Timothy R. Anderson 28.1 Introduction 443 28.2 Methodology 445 28.3 Application: Commercial Airplane Development 449 28.4 Conclusion and Matters for Future Work 454 References 455 29 DEA Score Confidence Intervals with Past–Present and Past–Present–Future-Based Resampling 459Kaoru Tone and Jamal Ouenniche 29.1 Introduction 459 29.2 Proposed Methodology 461 29.3 An Application to Healthcare 465 29.4 Conclusion 476 References 478 30 DEA Models Incorporating Uncertain Future Performance 480Tsung-Sheng Chang, Kaoru Tone and Chen-Hui Wu 30.1 Introduction 480 30.2 Generalized Dynamic Evaluation Structures 482 30.3 Future Performance Forecasts 484 30.4 Generalized Dynamic DEA Models 487 30.5 Empirical Study 495 30.6 Conclusions 513 References 514 31 Site Selection for the Next-Generation Supercomputing Center of Japan 516Kaoru Tone 31.1 Introduction 516 31.2 Hierarchical Structure and Group Decision by AHP 519 31.3 DEA Assurance Region Approach 521 31.4 Application to the Site Selection Problem 522 31.5 Decision and Conclusion 527 References 527 APPENDIX A: DEA-SOLVER-PRO 529 INDEX 535

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Book SynopsisThis book provides an introduction to index numbers for statisticians, economists and numerate members of the public. It covers the essential basics, mixing theoretical aspects with practical techniques to give a balanced and accessible introduction to the subject.Table of ContentsPreface xi Acknowledgements xv 1 Introduction 1 1.1 What is an index number? 1 1.2 Example – the Consumer Prices Index 2 1.3 Example – FTSE 100 5 1.4 Example – Multidimensional Poverty Index 6 1.5 Example – Gender Inequality Index 6 1.6 Representing the world with index numbers 7 1.7 Chapter summary 8 References 8 2 Index numbers and change 9 2.1 Calculating an index series from a data series 9 2.2 Calculating percentage change 11 2.3 Comparing data series with index numbers 13 2.4 Converting from an index series to a data series 14 2.5 Chapter summary 16 Exercise A 17 3 Measuring inflation 19 3.1 What is inflation? 19 3.2 What are inflation measures used for and why are they important? 20 3.2.1 Determination of monetary policy by a central bank 21 3.2.2 Changing of provisions for private pensions 21 3.2.3 Changes in amounts paid over long-term contracts 21 3.2.4 Changes in rail fares and other goods 22 3.2.5 Evaluating investment decisions 22 3.2.6 Inputs to economic research and analysis 23 3.2.7 Index-linked debt 23 3.2.8 Tax allowances 23 3.2.9 Targets for stability of the economy in an international context 23 3.3 Chapter summary 24 References 24 Exercise B 25 4 Introducing price and quantity 27 4.1 Measuring price change 27 4.2 Simple, un-weighted indices for price change 30 4.2.1 Simple price indices 30 4.2.2 Simple quantity indices 33 4.3 Price, quantity and value 34 4.4 Example – Retail Sales Index 35 4.5 Chapter summary 36 Exercise C 37 5 Laspeyres and Paasche indices 39 5.1 The Laspeyres price index 40 5.2 The Paasche price index 41 5.3 Laspeyres and Paasche quantity indices 43 5.4 Laspeyres and Paasche: mind your Ps and Qs 45 5.4.1 Laspeyres price index as a weighted sum of price relatives 45 5.4.2 Laspeyres quantity index as a weighted sum of quantity relatives 46 5.4.3 Paasche price index as a weighted harmonic mean of price relatives 46 5.4.4 Paasche quantity index as a weighted harmonic mean of quantity relatives 46 5.5 Laspeyres, Paasche and the Index Number Problem 48 5.6 Laspeyres or Paasche? 49 5.7 A more practical alternative to a Laspeyres price index? 51 5.8 Chapter summary 51 References 52 Exercise D 53 6 Domains and aggregation 55 6.1 Defining domains 55 6.2 Indices for domains 57 6.3 Aggregating domains 58 6.4 More complex aggregation structures 62 6.5 A note on aggregation structures in practice 62 6.6 Non-consistency in aggregation 63 6.7 Chapter summary 63 Exercise E 64 7 Linking and chain-linking 67 7.1 Linking 68 7.2 Re-basing 71 7.3 Chain-linking 74 7.4 Chapter summary 75 Exercise F 76 8 Constructing the consumer prices index 79 8.1 Specifying the index 79 8.2 The basket 80 8.3 Locations and outlets 81 8.4 Price collection 81 8.5 Weighting 81 8.6 Aggregation structure 82 8.7 Elementary aggregates 83 8.8 Linking 84 8.9 Owner occupier housing 85 8.10 Publication 85 8.11 Special procedures 86 8.12 Chapter summary 86 References 86 Exercise G 88 9 Re-referencing a series 89 9.1 Effective comparisons with index numbers 89 9.2 Changing the index reference period 92 9.3 Why re-reference? 94 9.4 Re-basing 95 9.5 Chapter summary 96 References 96 Exercise H 97 10 Deflation 99 10.1 Value at constant price 101 10.2 Volume measures in the national accounts 102 10.3 Chapter summary 103 Exercise I 104 11 Price and quantity index numbers in practice 105 11.1 A big picture view of price indices 105 11.2 The harmonised index of consumer prices 106 11.3 UK measures of consumer price inflation 107 11.4 PPI and SPPI 108 11.5 PPPs and international comparison 109 11.6 Quantity indices 109 11.7 Gross domestic product 110 11.8 Index of Production 111 11.9 Index of services 112 11.10 Retail sales index 113 11.11 Chapter summary 114 11.12 Data links 115 References 115 12 Further index formulae 119 12.1 Recap on price index formulae 119 12.2 Classifying price and quantity index formulae 120 12.3 Asymmetrically weighted price indices 120 12.4 Symmetric weighted price indices 123 12.5 Un-weighted price indices 124 12.6 Different formulae, different index numbers 126 12.7 Chapter summary 127 References 127 Exercise J 129 13 The choice of index formula 131 13.1 The index number problem 131 13.2 The axiomatic approach 133 13.3 The economic approach 134 13.4 The sampling approach 135 13.5 The stochastic approach to index numbers 136 13.6 Which approach is used in practice? 137 13.7 Chapter summary 138 References 138 Exercise K 140 14 Issues in index numbers 141 14.1 Cost-of-living versus cost-of-goods 141 14.2 Consumer behaviour and substitution 143 14.3 New and disappearing goods 144 14.4 Quality change 145 14.4.1 Option 1: do nothing – pure price change 146 14.4.2 Option 2: automatic linking – pure quality change 146 14.4.3 Option 3: linking 147 14.4.4 Option 4: imputation 147 14.4.5 Option 5: hedonics 147 14.5 Difficult to measure items 148 14.6 Chapter summary 149 References 149 15 Research topics in index numbers 151 15.1 The uses of scanner data 151 15.1.1 Improvements at the lowest level of aggregation 152 15.1.2 Understanding consumer behaviour 152 15.1.3 Alternative measurement schemes 153 15.1.4 Frequency of indices 153 15.2 Variations on indices 154 15.2.1 Regional indices 154 15.2.2 Variation by socio-economic group or income quantile 154 15.3 Difficult items 155 15.3.1 Clothing 155 15.3.2 New and disappearing goods 156 15.3.3 Hedonics 157 15.4 Chaining 157 15.5 Some research questions 158 References 158 A Mathematics for index numbers 161 A.1 Notation 161 A.1.1 Summation notation 161 A.1.2 An alternative representation 163 A.1.3 Geometric indices 164 A.1.4 Harmonic indices 164 A.2 Key results 165 A.2.1 The value ratio decomposition 165 A.2.2 Converting between the two forms of price and quantity indices 166 A.2.3 Other examples of the price-relative/weights 167 A.2.4 The value ratio as a product of Fisher indices 167 A.3 Index Formula Styles 168 B Choice of index formula 169 B.1 The axiomatic approach to index numbers 169 B.1.1 An introduction to the axiomatic approach 169 B.1.2 Some axioms 170 B.1.3 Choosing an index based on the axiomatic approach 173 B.1.4 Conclusions 174 B.2 The economic approach to index numbers 174 B.2.1 The economic approach to index numbers 174 B.2.2 A result on expenditure indices 177 B.2.3 Example 1: Cobb-Douglas and the Jevons index 179 B.2.4 Example 2: CES and the Lloyd-Moulton index 181 B.2.5 Issues with the economic approach 183 References 184 C Glossary of terms and formulas 185 C.1 Commonly used terms 185 C.2 Commonly used symbols 189 C.3 Unweighted indices (price versions only) 190 C.4 Weighted indices (price versions only) 191 D Solutions to exercises 193 E Further reading 211 E.1 Manuals 211 E.2 Books 211 E.3 Papers 212 Index 213

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Book SynopsisStatistics and the Evaluation of Evidence for Forensic Scientists The leading resource in the statistical evaluation and interpretation of forensic evidence The third edition of Statistics and the Evaluation of Evidence for Forensic Scientists is fully updated to provide the latest research and developments in the use of statistical techniques to evaluate and interpret evidence. Courts are increasingly aware of the importance of proper evidence assessment when there is an element of uncertainty. Because of the increasing availability of data, the role of statistical and probabilistic reasoning is gaining a higher profile in criminal cases. That's why lawyers, forensic scientists, graduate students, and researchers will find this book an essential resource, one which explores how forensic evidence can be evaluated and interpreted statistically. It's written as an accessible source of information for all those with an interest in the evaluation and interpretatiTrade Review"I hope that every forensic laboratory in the United States and Europe has a copy of this book, and that they rapidly wear out from repeated use. It is a tremendous resource. It could also be a valuable textbook for a methods course in criminology departments."—David Banks, Department of Statistical Science, Duke University, Durham, NC, USATable of ContentsForeword xvii Preface to Third Edition xxi Preface to Second Edition xxx Preface to First Edition xxxvii 1 Uncertainty in Forensic Science 1 1.1 Introduction 1 1.2 Statistics and the Law 3 1.3 Uncertainty in Scientific Evidence 11 1.3.1 The Frequentist Method 15 1.3.2 Stains of Body Fluids 17 1.3.3 Glass Fragments 21 1.4 Terminology 29 1.5 Types of Data 34 1.6 Populations 36 1.7 Probability 41 1.7.1 Introduction 41 1.7.2 A Standard for Uncertainty 46 1.7.3 Events 55 1.7.4 Classical and Frequentist Definitions of Probability and Their Limitations 57 1.7.5 Subjective Definition of Probability 60 1.7.6 The Quantification of Probability Through a Betting Scheme 64 1.7.7 Probabilities and Frequencies: The Role of Exchangeability 69 1.7.8 Laws of Probability 78 1.7.9 Dependent Events and Background Information 82 1.7.10 Law of Total Probability 91 1.7.11 Updating of Probabilities 96 2 The Evaluation of Evidence 101 2.1 Odds 101 2.1.1 Complementary Events 101 2.1.2 Examples 104 2.1.3 Definition of Odds 105 2.2 Bayes’ Theorem 108 2.2.1 Statement of the Theorem 109 2.2.2 Examples 109 2.3 The Odds Form of Bayes’ Theorem 121 2.3.1 Likelihood Ratio 121 2.3.2 Bayes’ Factor and Likelihood Ratio 125 2.3.3 Three-Way Tables 130 2.3.4 Logarithm of the Likelihood Ratio 134 2.4 The Value of Evidence 138 2.4.1 Evaluation of Forensic Evidence 138 2.4.2 Justification of the Use of the Likelihood Ratio 154 2.4.3 Single Value for the Likelihood Ratio 158 2.4.4 Role of Background Information 161 2.4.5 Summary of Competing Propositions 163 2.4.6 Qualitative Scale for the Value of the Evidence 168 2.5 Errors in Interpretation 180 2.5.1 Fallacy of the Transposed Conditional 186 2.5.2 Source Probability Error 190 2.5.3 Ultimate Issue Error 194 2.5.4 Defence Attorney’s Fallacy 194 2.5.5 Probability (Another Match) Error 196 2.5.6 Numerical Conversion Error 199 2.5.7 False Positive Fallacy 202 2.5.8 Expected Value Fallacy 203 2.5.9 Uniqueness 206 2.5.10 Other Difficulties 209 2.5.11 Empirical Evidence of Errors in Interpretation 220 2.6 Misinterpretations 233 2.7 Explanation of Transposed Conditional, Defence Attorney’s and False Positive Fallacies 236 2.7.1 Explanation of the Fallacy of the Transposed Conditional 236 2.7.2 Explanation of the Defence Attorney’s Fallacy 239 2.7.3 Explanation of the False Positive Fallacy 241 2.8 Making Coherent Decisions 245 2.8.1 Elements of Statistical Decision Theory 246 2.8.2 Decision Analysis: An Example 249 2.9 Graphical Probabilistic Models: Bayesian Networks 254 2.9.1 Elements of the Bayesian Networks 256 2.9.2 The Construction of Bayesian Networks 261 2.9.3 Bayesian Decision Networks (Influence Diagrams) 272 3 Historical Review 279 3.1 Early History 279 3.2 The Dreyfus Case 286 3.3 Statistical Arguments by Early Twentieth- Century Forensic Scientists 293 3.4 People v.Collins 299 3.5 Discriminating Power 307 3.5.1 Derivation 307 3.5.2 Evaluation of Evidence by Discriminating Power 310 3.5.3 Finite Samples 316 3.5.4 Combination of Independent Systems 319 3.5.5 Correlated Attributes 321 3.6 Significance Probabilities 325 3.6.1 Calculation of Significance Probabilities 326 3.6.2 Relationship to Likelihood Ratio 333 3.6.3 Combination of Significance Probabilities 338 3.7 Coincidence Probabilities 342 3.7.1 Introduction 342 3.7.2 Comparison Stage 346 3.7.3 Significance Stage 347 3.8 Likelihood Ratio 351 4 Bayesian Inference 359 4.1 Introduction 359 4.2 Inference for a Proportion 368 4.2.1 Interval Estimation 374 4.2.2 Estimation with Zero Occurrences in a Sample 381 4.2.3 Uncertainty on Sensitivity and Specificity 387 4.3 Sampling 392 4.3.1 Choice of Sample Size in Large Consignments 398 4.3.2 Choice of Sample Size in Small Consignments 413 4.4 Bayesian Networks for Sampling Inspection 420 4.4.1 Large Consignments 420 4.4.2 Small Consignments 425 4.5 Inference for a Normal Mean 429 4.5.1 Known Variance 431 4.5.2 Unknown Variance 438 4.5.3 Interval Estimation 445 4.6 Quantity Estimation 449 4.6.1 Predictive Approach in Small Consignments 452 4.6.2 Predictive Approach in Large Consignments 461 4.7 Decision Analysis 464 4.7.1 Standard Loss Functions 465 4.7.2 Decision Analysis for Forensic Sampling 471 5 Evidence and Propositions: Theory 483 5.1 The Choice of Propositions and Pre-Assessment 483 5.2 Levels of Propositions and Roles of the Forensic Scientist 485 5.3 The Formal Development of a Likelihood Ratio for Different Propositions and Discrete Characteristics 499 5.3.1 Likelihood Ratio with Source Level Propositions 499 5.3.2 Likelihood Ratio with Activity Level Propositions 519 5.3.3 Likelihood Ratio with Offence Level Propositions 553 5.4 Validation of Bayesian Network Structures: An Example 562 5.5 Pre-Assessment 568 5.5.1 Pre-assessment of the Case 568 5.5.2 Pre-assessment of Evidence 575 5.5.3 Pre-assessment: A Practical Example 576 5.6 Combination of Items of Evidence 592 5.6.1 A Difficulty in Combining Evidence: The Problem of Conjunction 594 5.6.2 Generic Patterns of Inference in Combining Evidence 598 6 Evidence and Propositions: Practice 615 6.1 Examples for Evaluation given Source Level Propositions 615 6.1.1 General Population 616 6.1.2 Particular Population 617 6.1.3 A Note on The Appropriate Databases for Evaluation Given Source Level Propositions 619 6.1.4 Two Trace Problem 627 6.1.5 Many Samples 633 6.1.6 Multiple Propositions 637 6.1.7 A Note on Biological Traces 654 6.1.8 Additional Considerations on Source Level Propositions 670 6.2 Examples for Evaluation given Activity Level Propositions 699 6.2.1 A Practical Approach to Fibres Evaluation 701 6.2.2 A Practical Approach to Glass Evaluation 704 6.2.3 The Assignment of Probabilities for Transfer Events 713 6.2.4 The Assignment of Probabilities for Background Traces 734 6.2.5 Presence of Material with Non-corresponding Features 739 6.2.6 Absence of Evidence for Activity Level Propositions 741 6.3 Examples for Evaluation given Offence Level Propositions 745 6.3.1 One Stain, k Offenders 745 6.3.2 Two Stains, One Offender 752 6.3.3 Paternity and The Combination of Likelihood Ratios 756 6.3.4 Probability of Paternity 762 6.3.5 Absence of Evidence for Offence Level Propositions 768 6.3.6 A Note on Relevance and Offence Level Propositions 773 6.4 Summary 774 6.4.1 Stain Known to Have Been Left by Offenders: Source-Level Propositions 774 6.4.2 Material Known to Have Been (or Not to Have Been) Left by Offenders: Activity-Level Propositions 777 6.4.3 Stain May Not Have Been Left by Offenders: Offence-Level Propositions 779 7 Data Analysis 783 7.1 Introduction 783 7.2 Theory for Discrete Data 785 7.2.1 Data of Independent Counts with a Poisson Distribution 787 7.2.2 Data of Independent Counts with a Binomial Distribution 791 7.2.3 Data of Independent Counts with a Multinomial Distribution 793 7.3 Theory for Continuous Univariate Data 798 7.3.1 Assessment of Similarity Only 802 7.3.2 Sources of Variation: Two-Level Models 808 7.3.3 Transfer Probability 810 7.4 Normal Between-Source Variation 814 7.4.1 Marginal Distribution of Measurements 814 7.4.2 Approximate Derivation of the Likelihood Ratio 817 7.4.3 Lindley’s Approach 820 7.4.4 Interpretation of Result 825 7.4.5 Examples 827 7.5 Non-normal Between-Source Variation 830 7.5.1 Estimation of a Probability Density Function 831 7.5.2 Kernel Density Estimation for Between-Source Data 842 7.5.3 Examples 844 7.6 Multivariate Analysis 849 7.6.1 Introduction 849 7.6.2 Multivariate Two-Level Models 851 7.6.3 A Note on Sensitivity 864 7.6.4 Case Study for Two-Level Data 865 7.6.5 Three-Level Models 876 7.7 Discrimination 882 7.7.1 Discrete Data 884 7.7.2 Continuous Data 889 7.7.3 Autocorrelated Data 893 7.7.4 Multivariate Data 894 7.7.5 Cut-Offs and Legal Thresholds 899 7.8 Score-Based Models 906 7.8.1 Example 910 7.9 Bayes’ Factor and Likelihood Ratio (cont.) 913 8 Assessment of the Performance of Methods for the Evaluation of Evidence 919 8.1 Introduction 919 8.2 Properties of Methods for Evaluation 928 8.3 General Topics Relating to Sample Size Estimation and to Assessment 933 8.3.1 Probability of Strong Misleading Evidence: A Sample Size Problem 933 8.3.2 Calibration 948 8.4 Assessment of Performance of a Procedure for the Calculation of the Likelihood Ratio 952 8.4.1 Histograms and Tippett Plots 956 8.4.2 False Positive Rates, False Negative Rates and DET Plots 959 8.4.3 Empirical Cross-Entropy 961 8.5 Case Study: Kinship Analysis 972 8.6 Conclusion 979 Appendix A Probability Distributions 981 A.1 Introduction 981 A.2 Probability Distributions for Counts 988 A.2.1 Probabilities 988 A.2.2 Summary Measures 990 A.2.3 Binomial Distribution 995 A.2.4 Multinomial Distribution 997 A.2.5 Hypergeometric Distribution 998 A.2.6 Poisson Distribution 1000 A.2.7 Beta-Binomial and Dirichlet-Multinomial Distributions 1002 A.3 Measurements 1005 A.3.1 Summary Statistics 1005 A.3.2 Normal Distribution 1007 A.3.3 Jeffreys’ Prior Distributions 1021 A.3.4 Student’s t-Distribution 1021 A.3.5 Gamma and Chi-Squared Distributions 1025 A.3.6 Inverse Gamma and Inverse Chi-Squared Distributions 1026 A.3.7 Beta Distribution 1028 A.3.8 Dirichlet Distribution 1032 A.3.9 Multivariate Normal Distribution and Correlation 1035 A.3.10 Wishart Distribution 1040 A.3.11 Inverse Wishart Distribution 1041 Appendix B Matrix Properties 1043 B.1 Matrix Terminology 1043 B.1.1 The Trace of a Square Matrix 1044 B.1.2 The Transpose of a Matrix 1044 B.1.3 Addition of Two Matrices 1045 B.1.4 Determinant of a Matrix 1045 B.1.5 Matrix Multiplication 1046 B.1.6 The Inverse of a Matrix 1048 B.1.7 Completion of the Square 1049 References 1051 Notation 1143 Cases 1157 Author Index 1163 Subject Index 1187

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Book SynopsisThe ability to analyze and interpret enormous amounts of data has become a prerequisite for success in allied healthcare and the health sciences. Now in its 11th edition, Biostatistics: A Foundation for Analysis in the Health Sciences continues to offer in-depth guidance toward biostatistical concepts, techniques, and practical applications in the modern healthcare setting. Comprehensive in scope yet detailed in coverage, this text helps students understandand appropriately useprobability distributions, sampling distributions, estimation, hypothesis testing, variance analysis, regression, correlation analysis, and other statistical tools fundamental to the science and practice of medicine. Clearly-defined pedagogical tools help students stay up-to-date on new material, and an emphasis on statistical software allows faster, more accurate calculation while putting the focus on the underlying concepts rather than the math. Students develop highly relevant skills in inferential and differential statistical techniques, equipping them with the ability to organize, summarize, and interpret large bodies of data. Suitable for both graduate and advanced undergraduate coursework, this text retains the rigor required for use as a professional reference.Table of ContentsPREFACE vii 1 INTRODUCTION TO BIOSTATISTICS 1 1.1 Introduction, 2 1.2 Basic Concepts and Definitions, 2 1.3 Measurement and Measurement Scales, 5 1.4 Sampling and Statistical Inference, 7 Exercises, 12 1.5 The Scientific Method, 13 Exercises, 15 1.6 Computers and Technology, 15 1.7 Summary, 16 Review Questions and Exercises, 16 References, 17 2 DESCRIPTIVE STATISTICS 18 2.1 Introduction, 19 2.2 The Ordered Array, 19 2.3 Frequency Tables, 21 Exercises, 25 2.4 Measures of Central Tendency, 29 2.5 Measures of Dispersion, 34 Exercises, 41 2.6 Visualizing Data, 43 Exercises, 51 2.7 Summary, 51 Summary of Formulas for Chapter 2, 51 Review Questions and Exercises, 53 References, 56 3 SOME BASIC PROBABILITY CONCEPTS 57 3.1 Introduction, 57 3.2 Two Views of Probability: Objective and Subjective, 58 3.3 Elementary Properties of Probability, 60 3.4 Calculating the Probability of an Event, 61 Exercises, 68 3.5 Bayes’ Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative, 69 Exercises, 73 3.6 Summary, 74 Summary of Formulas for Chapter 3, 75 Review Questions and Exercises, 76 References, 79 4 PROBABILITY DISTRIBUTIONS 80 4.1 Introduction, 81 4.2 Probability Distributions of Discrete Variables, 81 Exercises, 86 4.3 The Binomial Distribution, 87 Exercises, 95 4.4 The Poisson Distribution, 96 Exercises, 100 4.5 Continuous Probability Distributions, 101 4.6 The Normal Distribution, 103 Exercises, 109 4.7 Normal Distribution Applications, 109 Exercises, 113 4.8 Summary, 114 Summary of Formulas for Chapter 4, 114 Review Questions and Exercises, 115 References, 117 5 SOME IMPORTANT SAMPLING DISTRIBUTIONS 119 5.1 Introduction, 119 5.2 Sampling Distributions, 120 5.3 Distribution of the Sample Mean, 121 Exercises, 128 5.4 Distribution of the Difference between Two Sample Means, 129 Exercises, 133 5.5 Distribution of the Sample Proportion, 134 Exercises, 136 5.6 Distribution of the Difference between Two Sample Proportions, 137 Exercises, 139 5.7 Summary, 139 Summary of Formulas for Chapter 5, 140 Review Questions and Exercises, 140 References, 141 6 ESTIMATION 143 6.1 Introduction, 144 6.2 Confidence Interval for a Population Mean, 147 Exercises, 152 6.3 The t Distribution, 153 Exercises, 157 6.4 Confidence Interval for the Difference between Two Population Means, 158 Exercises, 164 6.5 Confidence Interval for a Population Proportion, 165 Exercises, 166 6.6 Confidence Interval for the Difference between Two Population Proportions, 167 Exercises, 168 6.7 Determination of Sample Size for Estimating Means, 169 Exercises, 171 6.8 Determination of Sample Size for Estimating Proportions, 171 Exercises, 172 6.9 The Chi-Square Distribution and the Confidence Interval for the Variance of a Normally Distributed Population, 173 Exercises, 177 6.10 The F-Distribution and the Confidence Interval for the Ratio of the Variances of Two Normally Distributed Populations, 177 Exercises, 180 6.11 Summary, 181 Summary of Formulas for Chapter 6, 182 Review Questions and Exercises, 183 References, 186 7 HYPOTHESIS TESTING 189 7.1 Introduction, 190 7.2 Hypothesis Testing: A Single Population Mean, 200 Exercises, 211 7.3 Hypothesis Testing: The Difference between Two Population Means, 213 Exercises, 221 7.4 Paired Comparisons, 224 Exercises, 229 7.5 Hypothesis Testing: A Single Population Proportion, 232 Exercises, 234 7.6 Hypothesis Testing: The Difference between Two Population Proportions, 235 Exercises, 236 7.7 Hypothesis Testing: A Single Population Variance, 238 Exercises, 240 7.8 Hypothesis Testing: The Ratio of Two Population Variances, 241 Exercises, 244 7.9 The Type II Error and the Power of a Test, 245 Exercises, 249 7.10 Determining Sample Size to Control Type II Errors, 249 Exercises, 251 7.11 Summary, 251 Summary of Formulas for Chapter 7, 252 Review Questions and Exercises, 254 References, 264 8 ANALYSIS OF VARIANCE 267 8.1 Introduction, 268 8.2 The Completely Randomized Design, 271 Exercises, 289 8.3 The Randomized Complete Block Design, 294 Exercises, 301 8.4 The Repeated Measures Design, 305 Exercises, 313 8.5 The Factorial Experiment, 315 Exercises, 326 8.6 Summary, 329 Summary of Formulas for Chapter 8, 329 Review Questions and Exercises, 331 References, 350 9 SIMPLE LINEAR REGRESSION AND CORRELATION 354 9.1 Introduction, 355 9.2 The Regression Model, 355 9.3 The Sample Regression Equation, 357 Exercises, 364 9.4 Evaluating the Regression Equation, 366 Exercises, 380 9.5 Using the Regression Equation, 380 Exercises, 384 9.6 The Correlation Model, 384 9.7 The Correlation Coefficient, 386 Exercises, 394 9.8 Some Precautions, 397 9.9 Summary, 398 Summary of Formulas for Chapter 9, 399 Review Questions and Exercises, 401 References, 413 10 MULTIPLE REGRESSION AND CORRELATION 416 10.1 Introduction, 417 10.2 The Multiple Linear Regression Model, 417 10.3 Obtaining the Multiple Regression Equation, 418 Exercises, 423 10.4 Evaluating the Multiple Regression Equation, 427 Exercises, 433 10.5 Using the Multiple Regression Equation, 433 Exercises, 435 10.6 The Multiple Correlation Model, 435 Exercises, 443 10.7 Summary, 446 Summary of Formulas for Chapter 10, 447 Review Questions and Exercises, 448 References, 454 11 REGRESSION ANALYSIS: SOME ADDITIONAL TECHNIQUES 455 11.1 Introduction, 455 11.2 Qualitative Independent Variables, 459 Exercises, 472 11.3 Variable Selection Procedures, 474 Exercises, 478 11.4 Logistic Regression, 485 Exercises, 495 11.5 Poisson Regression, 497 Exercises, 503 11.6 Summary, 504 Summary of Formulas for Chapter 11, 505 Review Questions and Exercises, 506 References, 517 12 ThE CHI-SQUARE DISTRIBUTION AND THE ANALYSIS OF FREQUENCIES 519 12.1 Introduction, 520 12.2 The Mathematical Properties of the Chi-Square Distribution, 520 12.3 Tests of Goodness-of-Fit, 523 Exercises, 533 12.4 Tests of Independence, 535 Exercises, 544 12.5 Tests of Homogeneity, 545 Exercises, 551 12.6 The Fisher’s Exact Test, 552 Exercises, 557 12.7 Relative Risk, Odds Ratio, and the Mantel–Haenszel Statistic, 557 Exercises, 567 12.8 Summary, 569 Summary of Formulas for Chapter 12, 570 Review Questions and Exercises, 571 References, 576 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS 579 13.1 Introduction, 580 13.2 Measurement Scales, 581 13.3 The Sign Test, 581 Exercises, 588 13.4 The Wilcoxon Signed-Rank Test for Location, 589 Exercises, 593 13.5 The Median Test, 594 Exercises, 596 13.6 The Mann–Whitney Test, 597 Exercises, 602 13.7 The Kolmogorov–Smirnov Goodness-of-Fit Test, 604 Exercises, 610 13.8 The Kruskal–Wallis One-Way Analysis of Variance by Ranks, 610 Exercises, 615 13.9 The Friedman Two-Way Analysis of Variance by Ranks, 618 Exercises, 622 13.10 The Spearman Rank Correlation Coefficient, 623 Exercises, 629 13.11 Nonparametric Regression Analysis, 631 Exercises, 634 13.12 Summary, 634 Summary of Formulas for Chapter 13, 635 Review Questions and Exercises, 636 References, 644 14 SURVIVAL ANALYSIS 646 14.1 Introduction, 647 14.2 Time-to-Event Data and Censoring, 647 14.3 The Kaplan–Meier Procedure, 651 Exercises, 656 14.4 Comparing Survival Curves, 658 Exercises, 661 14.5 Cox Regression: The Proportional Hazards Model, 663 Exercises, 666 14.6 Summary, 667 Summary of Formulas for Chapter 14, 667 Review Questions and Exercises, 668 References, 669 15 VITAL STATISTICS 671 15.1 Introduction, 671 15.2 Death Rates and Ratios, 672 Exercises, 677 15.3 Measures of Fertility, 679 Exercises, 681 15.4 Measures of Morbidity, 682 Exercises, 683 15.5 Summary, 683 Summary of Formulas for Chapter 15, 684 Review Questions and Exercises, 685 References, 686 INDEX 689 The following supplements are available through your instructor APPENDIX: STATISTICAL TABLES ANSWERS TO SELECTED PROBLEMS

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Book SynopsisA comprehensive and timely edition on an emerging new trend in time series Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH sets a strong foundation, in terms of distribution theory, for the linear model (regression and ANOVA), univariate time series analysis (ARMAX and GARCH), and some multivariate models associated primarily with modeling financial asset returns (copula-based structures and the discrete mixed normal and Laplace). It builds on the author''s previous book, Fundamental Statistical Inference: A Computational Approach, which introduced the major concepts of statistical inference. Attention is explicitly paid to application and numeric computation, with examples of Matlab code throughout. The code offers a framework for discussion and illustration of numerics, and shows the mapping from theory to computation. The topic of time series analysis is on firm footing, with numerous textbooks and research journals dedTable of ContentsPreface xiii Part I Linear Models: Regression and ANOVA 1 1 The Linear Model 3 1.1 Regression, Correlation, and Causality 3 1.2 Ordinary and Generalized Least Squares 7 1.2.1 Ordinary Least Squares Estimation 7 1.2.2 Further Aspects of Regression and OLS 8 1.2.3 Generalized Least Squares 12 1.3 The Geometric Approach to Least Squares 17 1.3.1 Projection 17 1.3.2 Implementation 22 1.4 Linear Parameter Restrictions 26 1.4.1 Formulation and Estimation 27 1.4.2 Estimability and Identifiability 30 1.4.3 Moments and the Restricted GLS Estimator 32 1.4.4 Testing With h = 0 34 1.4.5 Testing With Nonzero h 37 1.4.6 Examples 37 1.4.7 Confidence Intervals 42 1.5 Alternative Residual Calculation 47 1.6 Further Topics 51 1.7 Problems 56 1.A Appendix: Derivation of the BLUS Residual Vector 60 1.B Appendix: The Recursive Residuals 64 1.C Appendix: Solutions 66 2 Fixed Effects ANOVA Models 77 2.1 Introduction: Fixed, Random, and Mixed Effects Models 77 2.2 Two Sample t-Tests for Differences in Means 78 2.3 The Two Sample t-Test with Ignored Block Effects 84 2.4 One-Way ANOVA with Fixed Effects 87 2.4.1 The Model 87 2.4.2 Estimation and Testing 88 2.4.3 Determination of Sample Size 91 2.4.4 The ANOVA Table 93 2.4.5 Computing Confidence Intervals 97 2.4.6 A Word on Model Assumptions 103 2.5 Two-Way Balanced Fixed Effects ANOVA 107 2.5.1 The Model and Use of the Interaction Terms 107 2.5.2 Sums of Squares Decomposition without Interaction 108 2.5.3 Sums of Squares Decomposition with Interaction 113 2.5.4 Example and Codes 117 3 Introduction to Random and Mixed Effects Models 127 3.1 One-Factor Balanced Random Effects Model 128 3.1.1 Model and Maximum Likelihood Estimation 128 3.1.2 Distribution Theory and ANOVA Table 131 3.1.3 Point Estimation, Interval Estimation, and Significance Testing 137 3.1.4 Satterthwaite’s Method 139 3.1.5 Use of SAS 142 3.1.6 Approximate Inference in the Unbalanced Case 143 3.1.6.1 Point Estimation in the Unbalanced Case 144 3.1.6.2 Interval Estimation in the Unbalanced Case 150 3.2 Crossed Random Effects Models 152 3.2.1 Two Factors 154 3.2.1.1 With Interaction Term 154 3.2.1.2 Without Interaction Term 157 3.2.2 Three Factors 157 3.3 Nested Random Effects Models 162 3.3.1 Two Factors 162 3.3.1.1 Both Effects Random: Model and Parameter Estimation 162 3.3.1.2 Both Effects Random: Exact and Approximate Confidence Intervals 167 3.3.1.3 Mixed Model Case 170 3.3.2 Three Factors 174 3.3.2.1 All Effects Random 174 3.3.2.2 Mixed: Classes Fixed 176 3.3.2.3 Mixed: Classes and Subclasses Fixed 177 3.4 Problems 177 3.A Appendix: Solutions 178 Part II Time-Series Analysis: ARMAX Processes 185 4 The AR(1) Model 187 4.1 Moments and Stationarity 188 4.2 Order of Integration and Long-Run Variance 195 4.3 Least Squares and ML Estimation 196 4.3.1 OLS Estimator of a 196 4.3.2 Likelihood Derivation I 196 4.3.3 Likelihood Derivation II 198 4.3.4 Likelihood Derivation III 198 4.3.5 Asymptotic Distribution 199 4.4 Forecasting 200 4.5 Small Sample Distribution of the OLS and ML Point Estimators 204 4.6 Alternative Point Estimators of a 208 4.6.1 Use of the Jackknife for Bias Reduction 208 4.6.2 Use of the Bootstrap for Bias Reduction 209 4.6.3 Median-Unbiased Estimator 211 4.6.4 Mean-Bias Adjusted Estimator 211 4.6.5 Mode-Adjusted Estimator 212 4.6.6 Comparison 213 4.7 Confidence Intervals for a 215 4.8 Problems 219 5 Regression Extensions: AR(1) Errors and Time-varying Parameters 223 5.1 The AR(1) Regression Model and the Likelihood 223 5.2 OLS Point and Interval Estimation of a 225 5.3 Testing a = 0 in the ARX(1) Model 229 5.3.1 Use of Confidence Intervals 229 5.3.2 The Durbin–Watson Test 229 5.3.3 Other Tests for First-order Autocorrelation 231 5.3.4 Further Details on the Durbin–Watson Test 236 5.3.4.1 The Bounds Test, and Critique of Use of p-Values 236 5.3.4.2 Limiting Power as a → ±1 239 5.4 Bias-Adjusted Point Estimation 243 5.5 Unit Root Testing in the ARX(1) Model 246 5.5.1 Null is a = 1 248 5.5.2 Null is a < 1 256 5.6 Time-Varying Parameter Regression 259 5.6.1 Motivation and Introductory Remarks 260 5.6.2 The Hildreth–Houck Random Coefficient Model 261 5.6.3 The TVP Random Walk Model 269 5.6.3.1 Covariance Structure and Estimation 271 5.6.3.2 Testing for Parameter Constancy 274 5.6.4 Rosenberg Return to Normalcy Model 277 6 Autoregressive and Moving Average Processes 281 6.1 AR(p) Processes 281 6.1.1 Stationarity and Unit Root Processes 282 6.1.2 Moments 284 6.1.3 Estimation 287 6.1.3.1 Without Mean Term 287 6.1.3.2 Starting Values 290 6.1.3.3 With Mean Term 292 6.1.3.4 Approximate Standard Errors 293 6.2 Moving Average Processes 294 6.2.1 MA(1) Process 294 6.2.2 MA(q) Processes 299 6.3 Problems 301 6.A Appendix: Solutions 302 7 ARMA Processes 311 7.1 Basics of ARMA Models 311 7.1.1 The Model 311 7.1.2 Zero Pole Cancellation 312 7.1.3 Simulation 313 7.1.4 The ARIMA(p, d, q) Model 314 7.2 Infinite AR and MA Representations 315 7.3 Initial Parameter Estimation 317 7.3.1 Via the Infinite AR Representation 318 7.3.2 Via Infinite AR and Ordinary Least Squares 318 7.4 Likelihood-Based Estimation 322 7.4.1 Covariance Structure 322 7.4.2 Point Estimation 324 7.4.3 Interval Estimation 328 7.4.4 Model Mis-specification 330 7.5 Forecasting 331 7.5.1 AR(p) Model 331 7.5.2 MA(q) and ARMA(p, q) Models 335 7.5.3 ARIMA(p, d, q) Models 339 7.6 Bias-Adjusted Point Estimation: Extension to the ARMAX(1, q) model 339 7.7 Some ARIMAX Model Extensions 343 7.7.1 Stochastic Unit Root 344 7.7.2 Threshold Autoregressive Models 346 7.7.3 Fractionally Integrated ARMA (ARFIMA) 347 7.8 Problems 349 7.A Appendix: Generalized Least Squares for ARMA Estimation 351 7.B Appendix: Multivariate AR(p) Processes and Stationarity, and General Block Toeplitz Matrix Inversion 357 8 Correlograms 359 8.1 Theoretical and Sample Autocorrelation Function 359 8.1.1 Definitions 359 8.1.2 Marginal Distributions 365 8.1.3 Joint Distribution 371 8.1.3.1 Support 371 8.1.3.2 Asymptotic Distribution 372 8.1.3.3 Small-Sample Joint Distribution Approximation 375 8.1.4 Conditional Distribution Approximation 381 8.2 Theoretical and Sample Partial Autocorrelation Function 384 8.2.1 Partial Correlation 384 8.2.2 Partial Autocorrelation Function 389 8.2.2.1 TPACF: First Definition 389 8.2.2.2 TPACF: Second Definition 390 8.2.2.3 Sample Partial Autocorrelation Function 392 8.3 Problems 396 8.A Appendix: Solutions 397 9 ARMA Model Identification 405 9.1 Introduction 405 9.2 Visual Correlogram Analysis 407 9.3 Significance Tests 412 9.4 Penalty Criteria 417 9.5 Use of the Conditional SACF for Sequential Testing 421 9.6 Use of the Singular Value Decomposition 436 9.7 Further Methods: Pattern Identification 439 Part III Modeling Financial Asset Returns 443 10 Univariate GARCH Modeling 445 10.1 Introduction 445 10.2 Gaussian GARCH and Estimation 450 10.2.1 Basic Properties 451 10.2.2 Integrated GARCH 452 10.2.3 Maximum Likelihood Estimation 453 10.2.4 Variance Targeting Estimator 459 10.3 Non-Gaussian ARMA-APARCH, QMLE, and Forecasting 459 10.3.1 Extending the Volatility, Distribution, and Mean Equations 459 10.3.2 Model Mis-specification and QMLE 464 10.3.3 Forecasting 467 10.4 Near-Instantaneous Estimation of NCT-APARCH(1,1) 468 10.5 S𝛼,𝛽-APARCH and Testing the IID Stable Hypothesis 473 10.6 Mixed Normal GARCH 477 10.6.1 Introduction 477 10.6.2 The MixN(k)-GARCH(r, s) Model 478 10.6.3 Parameter Estimation and Model Features 479 10.6.4 Time-Varying Weights 482 10.6.5 Markov Switching Extension 484 10.6.6 Multivariate Extensions 484 11 Risk Prediction and Portfolio Optimization 487 11.1 Value at Risk and Expected Shortfall Prediction 487 11.2 MGARCH Constructs Via Univariate GARCH 493 11.2.1 Introduction 493 11.2.2 The Gaussian CCC and DCC Models 494 11.2.3 Morana Semi-Parametric DCC Model 497 11.2.4 The COMFORT Class 499 11.2.5 Copula Constructions 503 11.3 Introducing Portfolio Optimization 504 11.3.1 Some Trivial Accounting 504 11.3.2 Markowitz and DCC 510 11.3.3 Portfolio Optimization Using Simulation 513 11.3.4 The Univariate Collapsing Method 516 11.3.5 The ES Span 521 12 Multivariate t Distributions 525 12.1 Multivariate Student’s t 525 12.2 Multivariate Noncentral Student’s t 530 12.3 Jones Multivariate t Distribution 534 12.4 Shaw and Lee Multivariate t Distributions 538 12.5 The Meta-Elliptical t Distribution 540 12.5.1 The FaK Distribution 541 12.5.2 The AFaK Distribution 542 12.5.3 FaK and AFaK Estimation: Direct Likelihood Optimization 546 12.5.4 FaK and AFaK Estimation: Two-Step Estimation 548 12.5.5 Sums of Margins of the AFaK 555 12.6 MEST: Marginally Endowed Student’s t 556 12.6.1 SMESTI Distribution 557 12.6.2 AMESTI Distribution 558 12.6.3 MESTI Estimation 561 12.6.4 AoNm-MEST 564 12.6.5 MEST Distribution 573 12.7 Some Closing Remarks 574 12.A ES of Convolution of AFaK Margins 575 12.B Covariance Matrix for the FaK 581 13 Weighted Likelihood 587 13.1 Concept 587 13.2 Determination of Optimal Weighting 592 13.3 Density Forecasting and Backtest Overfitting 594 13.4 Portfolio Optimization Using (A)FaK 600 14 Multivariate Mixture Distributions 611 14.1 The Mixk Nd Distribution 611 14.1.1 Density and Simulation 612 14.1.2 Motivation for Use of Mixtures 612 14.1.3 Quasi-Bayesian Estimation and Choice of Prior 614 14.1.4 Portfolio Distribution and Expected Shortfall 620 14.2 Model Diagnostics and Forecasting 623 14.2.1 Assessing Presence of a Mixture 623 14.2.2 Component Separation and Univariate Normality 625 14.2.3 Component Separation and Multivariate Normality 629 14.2.4 Mixed Normal Weighted Likelihood and Density Forecasting 631 14.2.5 Density Forecasting: Optimal Shrinkage 633 14.2.6 Moving Averages of 𝜆 640 14.3 MCD for Robustness and Mix2Nd Estimation 645 14.4 Some Thoughts on Model Assumptions and Estimation 647 14.5 The Multivariate Laplace and Mixk Lapd Distributions 649 14.5.1 The Multivariate Laplace and EM Algorithm 650 14.5.2 The Mixk Lapd and EM Algorithm 654 14.5.3 Estimation via MCD Split and Forecasting 658 14.5.4 Estimation of Parameter b 660 14.5.5 Portfolio Distribution and Expected Shortfall 662 14.5.6 Fast Evaluation of the Bessel Function 663 Part IV Appendices 667 Appendix A Distribution of Quadratic Forms 669 A.1 Distribution and Moments 669 A.1.1 Probability Density and Cumulative Distribution Functions 669 A.1.2 Positive Integer Moments 671 A.1.3 Moment Generating Functions 673 A.2 Basic Distributional Results 677 A.3 Ratios of Quadratic Forms in Normal Variables 679 A.3.1 Calculation of the CDF 680 A.3.2 Calculation of the PDF 681 A.3.2.1 Numeric Differentiation 682 A.3.2.2 Use of Geary’s formula 682 A.3.2.3 Use of Pan’s Formula 683 A.3.2.4 Saddlepoint Approximation 685 A.4 Problems 689 A.A Appendix: Solutions 690 Appendix B Moments of Ratios of Quadratic Forms 695 B.1 For X ∼ Nn(0, 2I) and B = I 695 B.2 For X ∼ N(0, Σ) 708 B.3 For X ∼ N(𝜇, I) 713 B.4 For X ∼ N(𝜇, Σ) 720 B.5 Useful Matrix Algebra Results 725 B.6 Saddlepoint Equivalence Result 729 Appendix C Some Useful Multivariate Distribution Theory 733 C.1 Student’s t Characteristic Function 733 C.2 Sphericity and Ellipticity 739 C.2.1 Introduction 739 C.2.2 Sphericity 740 C.2.3 Ellipticity 748 C.2.4 Testing Ellipticity 768 Appendix D Introducing the SAS Programming Language 773 D.1 Introduction to SAS 774 D.1.1 Background 774 D.1.2 Working with SAS on a PC 775 D.1.3 Introduction to the Data Step and the Program Data Vector 777 D.2 Basic Data Handling 783 D.2.1 Method 1 784 D.2.2 Method 2 785 D.2.3 Method 3 786 D.2.4 Creating Data Sets from Existing Data Sets 787 D.2.5 Creating Data Sets from Procedure Output 788 D.3 Advanced Data Handling 790 D.3.1 String Input and Missing Values 790 D.3.2 Using set with first.var and last.var 791 D.3.3 Reading in Text Files 795 D.3.4 Skipping over Headers 796 D.3.5 Variable and Value Labels 796 D.4 Generating Charts, Tables, and Graphs 797 D.4.1 Simple Charting and Tables 798 D.4.2 Date and Time Formats/Informats 801 D.4.3 High Resolution Graphics 803 D.4.3.1 The GPLOT Procedure 803 D.4.3.2 The GCHART Procedure 805 D.4.4 Linear Regression and Time-Series Analysis 806 D.5 The SAS Macro Processor 809 D.5.1 Introduction 809 D.5.2 Macro Variables 810 D.5.3 Macro Programs 812 D.5.4 A Useful Example 814 D.5.4.1 Method 1 814 D.5.4.2 Method 2 816 D.6 Problems 817 D.7 Appendix: Solutions 819 Bibliography 825 Index 875

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Book SynopsisTable of ContentsPreface 1 Introduction to Statistics and Business Analytics 2 Visualizing Data with Charts and Graphs 3 Descriptive Statistics 4 Probability 5 Discrete Distributions 6 Continuous Distributions 7 Sampling and Sampling Distributions 8 Statistical Inference: Estimation for Single Populations 9 Statistical Inference: Hypothesis Testing for Single Populations 10 Statistical Inferences About Two Populations 11 Analysis of Variance and Design of Experiments 12 Simple Regression Analysis and Correlation 13 Multiple Regression Analysis 14 Building Multiple Regression Models 15 Time-Series Forecasting and Index Numbers 16 Analysis of Categorical Data 17 Nonparametric Statistics 18 Statistical Quality Control 19 Decision Analysis Appendix A Tables Appendix Glossary B Answers to Selected Odd-Numbered Quantitative Problems Index

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Book SynopsisTable of ContentsPreliminaries Introduction to Statistical Investigations 1 Section P.1: Introduction to the Six-Step Method 2 Example P.1: Organ Donations 2 Section P.2: Exploring Data 7 Example P.2: Oh, Say Can You Sing? 7 Section P.3: Exploring Random Processes 14 Exploration P.3: Cars or Goats 14 Unit 1 Four Pillars of Inference: Strength, Size, Breadth, and Cause 30 1 Significance: How Strong Is the Evidence? 31 Section 1.1: Introduction to Chance Models 32 Example 1.1: Can Dolphins Communicate? 33 Exploration 1.1: Can Dogs Understand Human Cues? 41 Section 1.2: Measuring the Strength of Evidence 45 Example 1.2: Rock-Paper-Scissors 46 Exploration 1.2: Tasting Water 52 Section 1.3: Alternative Measure of Strength of Evidence 57 Example 1.3: Heart Transplant Operations 58 Exploration 1.3: Do People Use Facial Prototyping? 62 Section 1.4: What Impacts Strength of Evidence? 66 Example 1.4: Predicting Elections from Faces? 66 Exploration 1.4: Competitive Advantage to Uniform Colors? 72 Section 1.5: Inference for a Single Proportion: Theory-Based Approach 75 Example 1.5: Halloween Treats 77 Exploration 1.5: Eye Dominance 80 2 Generalization: How Broadly Do the Results Apply? 117 Section 2.1: Sampling from a Finite Population: Proportions 118 Example 2.1: Voter Turnout 119 Exploration 2.1: Sampling Words 126 Section 2.2: Quantitative Data 133 Example 2.2: Sampling Students 134 Exploration 2.2: Sampling Words (cont.) 138 Section 2.3: Theory-based Inference for a Population Mean 143 Example 2.3: Estimating Elapsed Time 143 Exploration 2.3: Sleepless Nights? 150 Section 2.4: Other Statistics 154 Example 2.4: Estimating Elapsed Time (cont.) 154 Exploration 2.4: Backpack Weights 160 3 Estimation: How Large Is the Effect? 187 Section 3.1: Statistical Inference: Confidence Intervals 188 Example 3.1: Can Dogs Sniff Out Cancer? 189 Exploration 3.1: Kissing Right? 194 Section 3.2: 2SD and Theory-Based Confidence Intervals for a Single Proportion 198 Example 3.2: Cyberbullying 198 Exploration 3.2: How Mobile Are We? 203 Section 3.3: 2SD and Theory-Based Confidence Intervals for a Single Mean 207 Example 3.3: Used Cars 207 Exploration 3.3: Sleepless Nights? (cont.) 210 Section 3.4: Factors That Affect the Width of a Confidence Interval 213 Example 3.4: American Cat Ownership 214 Exploration 3.4A: Holiday Spending Habits 216 Exploration 3.4B: Reese’s Pieces 218 4 Causation: Can We Say What Caused the Effect? 245 Section 4.1: Association and Confounding 246 Example 4.1: Night Lights and Nearsightedness 247 Exploration 4.1: Home Court Disadvantage? 250 Section 4.2: Observational Studies Versus Experiments 252 Example 4.2: Lying on the Internet 253 Exploration 4.2: Have a Nice Trip 257 Unit 2 Comparing Two Groups 278 5 Comparing Two Proportions 279 Section 5.1: Comparing Two Groups: Categorical Response 280 Example 5.1: Buckling Up? 280 Exploration 5.1: Murderous Nurse? 285 Section 5.2: Comparing Two Proportions: Simulation-Based Approach 288 Example 5.2: Swimming with Dolphins 289 Exploration 5.2: Is Yawning Contagious? 297 Section 5.3: Comparing Two Proportions: Theory-Based Approach 304 Example 5.3: Parents’ Smoking Status and Their Babies’ Sex 305 Exploration 5.3: Donating Blood 311 6 Comparing Two Means 346 Section 6.1: Comparing Two Groups: Quantitative Response 347 Example 6.1: Geyser Eruptions 347 Exploration 6.1: Cancer Pamphlets 350 Section 6.2: Comparing Two Means: Simulation-Based Approach 354 Example 6.2: Dung Beetles 354 Exploration 6.2: Lingering Effects of Sleep Deprivation 363 Section 6.3: Comparing Two Means: Theory-Based Approach 369 Example 6.3: Violent Video Games and Aggression 369 Exploration 6.3: Close Friends 378 7 Paired Data: One Quantitative Variable 407 Section 7.1: Paired Designs 408 Example 7.1: Can You Study with Music Blaring? 408 Exploration 7.1: Rounding First Base 411 Section 7.2: Simulation-Based Approach to Analyzing Paired Data 413 Example 7.2: Rounding First Base (cont.) 414 Exploration 7.2: Exercise and Heart Rate 420 Section 7.3: Theory-Based Approach to Analyzing Data from Paired Samples 425 Example 7.3: Dad Jokes? 425 Exploration 7.3: Comparing Auction Formats 431 Unit 3 Analyzing More General Situations 456 8 Comparing More Than Two Proportions 458 Section 8.1: Comparing Multiple Proportions: Simulation-Based Approach 459 Example 8.1: Coming to a Stop 460 Exploration 8.1: Recruiting Organ Donors 466 Section 8.2: Comparing Multiple Proportions: Theory-Based Approach 470 Example 8.2: Sham Acupuncture 471 Exploration 8.2A: Conserving Hotel Towels 476 Exploration 8.2B: Nearsightedness and Night Lights Revisited 480 Section 8.3: Chi-Square Goodness-of-Fit Test 484 Example 8.3: Fair Die? 484 Exploration 8.3: Are Birthdays Equally Distributed Throughout the Week? 490 9 Comparing More Than Two Means 519 Section 9.1: Comparing Multiple Means: Simulation- Based Approach 520 Example 9.1: Comprehending Ambiguous Prose 520 Exploration 9.1: Exercise and Brain Volume 525 Section 9.2: Comparing Multiple Means: Theory-Based Approach 529 Example 9.2: Recalling Ambiguous Prose 530 Exploration 9.2: Comparing Popular Diets 538 10 Two Quantitative Variables 565 Section 10.1: Two Quantitative Variables: Scatterplots and Correlation 566 Example 10.1: Why Whales Are Big, but Not Bigger 567 Exploration 10.1: Height and Winning at Tennis 571 Section 10.2: Inference for the Correlation Coefficient: Simulation-Based Approach 576 Example 10.2: Exercise Intensity and Mood Changes 576 Exploration 10.2: Draft Lottery 580 Section 10.3: Least Squares Regression 585 Example 10.3: Height and Winning at Tennis (cont.) 585 Exploration 10.3: Predicting Height from Footprints 590 Section 10.4: Inference for the Regression Slope: Simulation-Based Approach 596 Example 10.4: Do Students Who Spend More Time in Non-Academic Activities Tend to Have Lower GPAs? 596 Exploration 10.4: Predicting Brain Density from Number of Facebook Friends 599 Section 10.5: Inference for the Regression Slope: Theory-Based Approach 601 Example 10.5A: Predicting Heart Rate from Body Temperature 602 Example 10.5B: Smoking and Drinking 606 Exploration 10.5: Predicting Brain Density from Number of Facebook Friends (cont.) 608 Unit 4 Probability (Online) 11-1 11 Modeling Randomness 11-2 Section 11.1: Basics of Probability 11-3 Example 11.1: Random Ice Cream Prices 11-3 Exploration 11.1: Random Babies 11-8 Section 11.2: Probability Rules 11-10 Example 11.2: Watching Films 11-11 Exploration 11.2: Random Ice Cream Prices (cont.) 11-15 Section 11.3: Conditional Probability and Independence 11-19 Example 11.3: Watching Films Revisited 11-20 Exploration 11.3A: College Admissions 11-25 Exploration 11.3B: Rare Disease Testing 11-28 Section 11.4: Discrete Random Variables 11-30 Example 11.4: A Game of Chance 11-30 Exploration 11.4: Traffic Lights 11-35 Section 11.5: Random Variable Rules 11-38 Example 11.5: A Game of Chance Revisited 11-38 Exploration 11.5: Skee-Ball 11-45 Section 11.6: Binomial and Geometric Random Variables 11-50 Example 11.6: Time to Leave the Nest? 11-52 Exploration 11.6: Clueless Quiz 11-59 Section 11.7: Continuous Random Variables and Normal Distributions 11-63 Example 11.7: Heights of Adult Women 11-65 Exploration 11.7A: Birthweights 11-69 Exploration 11.7B: Run, Girl, Run! 11-71 Section 11.8: Revisiting Theory-Based Approximations of Sampling Distributions 11-72 Example 11.8A: Time to Leave the Nest Revisited 11-74 Example 11.8B: Intelligence Test 11-75 Exploration 11.8A: Racket Spinning 11-77 Exploration 11.8B: Random Ice Cream Prices (cont.) 11-77 Appendix A Calculation Details 645 Appendix B Stratified and Cluster Samples 662 Solutions to Selected Exercises 666 Index 728

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Book SynopsisTable of ContentsPreface xv Introduction 1 Why Study Probability? 1 Software Use in Probability 2 Modern Application of Classic Probability Problems 2 Applications to Business 3 Applications to the Life Sciences 4 Applications to Engineering and Operations Research 4 Applications to Finance 6 Probability in Everyday Life 7 1 Introduction to Probability 13 Introduction 13 1.1 Sample Spaces and Events 13 The Sample Space of an Experiment 13 Events 15 Some Relations from Set Theory 16 Exercises Section 1.1 (1–12) 18 1.2 Axioms Interpretations and Properties of Probability 19 Interpreting Probability 21 More Probability Properties 23 Contingency Tables 25 Determining Probabilities Systematically 26 Equally Likely Outcomes 27 Exercises Section 1.2 (13–30) 28 1.3 Counting Methods 30 The Fundamental Counting Principle 31 Tree Diagrams 32 Permutations 33 Combinations 34 Partitions 38 Exercises Section 1.3 (31–50) 39 Supplementary Exercises (51–62) 42 2 Conditional Probability and Independence 45 Introduction 45 2.1 Conditional Probability 45 The Definition of Conditional Probability 46 The Multiplication Rule for P(A ∩ B) 49 2.2 The Law of Total Probability and Bayes’ Theorem 52 The Law of Total Probability 52 Bayes’ Theorem 55 Exercises Section 2.2 (17–32) 59 2.3 Independence 61 The Multiplication Rule for Independent Events 63 Independence of More Than Two Events 65 Exercises Section 2.3 (33–54) 66 2.4 Simulation of Random Events 69 The Backbone of Simulation: Random Number Generators 70 Precision of Simulation 73 Exercises Section 2.4 (55–74) 74 Supplementary Exercises (75–100) 77 3 Discrete Probability Distributions:general Properties 82 Introduction 82 3.1 Random Variables 82 Two Types of Random Variables 84 Exercises Section 3.1 (1–10) 85 3.2 Probability Distributions for Discrete Random Variables 86 Another View of Probability Mass Functions 89 Exercises Section 3.2 (11–21) 90 3.3 The Cumulative Distribution Function 91 Exercises Section 3.3 (22–30) 95 3.4 Expected Value and Standard Deviation 96 The Expected Value of X 97 The Expected Value of a Function 99 The Variance and Standard Deviation of X 102 Properties of Variance 104 Exercises Section 3.4 (31–50) 105 3.5 Moments and Moment Generating Functions 108 The Moment Generating Function 109 Obtaining Moments from the MGF 111 Exercises Section 3.5 (51–64) 113 3.6 Simulation of Discrete Random Variables 114 Simulations Implemented in R and Matlab 117 Simulation Mean Standard Deviation and Precision 117 Exercises Section 3.6 (65–74) 119 Supplementary Exercises (75–84) 120 4 Families of Discrete Distributions 122 Introduction 122 4.1 Parameters and Families of Distributions 122 Exercises Section 4.1 (1–6) 124 4.2 The Binomial Distribution 125 The Binomial Random Variable and Distribution 127 Computing Binomial Probabilities 129 The Mean Variance and Moment Generating Function 130 Binomial Calculations with Software 132 Exercises Section 4.2 (7–34) 132 4.3 The Poisson Distribution 136 The Poisson Distribution as a Limit 137 The Mean Variance and Moment Generating Function 139 The Poisson Process 140 Poisson Calculations with Software 141 Exercises Section 4.3 (35–54) 142 4.4 The Hypergeometric Distribution 145 Mean and Variance 148 Hypergeometric Calculations with Software 149 Exercises Section 4.4 (55–64) 149 4.5 The Negative Binomial and Geometric Distributions 151 The Geometric Distribution 152 Mean Variance and Moment Generating Function 152 Alternative Definitions of the Negative Binomial Distribution 153 Negative Binomial Calculations with Software 154 Exercises Section 4.5 (65–78) 154 Supplementary Exercises (79–100) 156 5 Continuous Probability Distributions:general Properties 160 Introduction 160 5.1 Continuous Random Variables and Probability Density Functions 160 Probability Distributions for Continuous Variables 161 Exercises Section 5.1 (1–8) 165 5.2 The Cumulative Distribution Function and Percentiles 166 Using F(x) to Compute Probabilities 168 Obtaining f(x) fromF(x) 169 Percentiles of a Continuous Distribution 169 Exercises Section 5.2 (9–18) 171 5.3 Expected Values Variance and Moment Generating Functions 173 Expected Values 173 Variance and Standard Deviation 175 Properties of Expectation and Variance 176 Moment Generating Functions 177 Exercises Section 5.3 (19–38) 179 5.4 Transformation of a Random Variable 181 Exercises Section 5.4 (39–54) 185 5.5 Simulation of Continuous Random Variables 186 The Inverse CDF Method 186 The Accept–Reject Method 189 Precision of Simulation Results 191 Exercises Section 5.5 (55–63) 191 Supplementary Exercises (64–76) 193 6 Families of Continuous Distributions 196 Introduction 196 6.1 The Normal (Gaussian) Distribution 196 The Standard Normal Distribution 197 Arbitrary Normal Distributions 199 The Moment Generating Function 203 Normal Distribution Calculations with Software 204 Exercises Section 6.1 (1–27) 205 6.2 Normal Approximation of Discrete Distributions 208 Approximating the Binomial Distribution 209 Exercises Section 6.2 (28–36) 211 6.3 The Exponential and Gamma Distributions 212 The Exponential Distribution 212 The Gamma Distribution 214 The Gamma and Exponential MGFs 217 Gamma and Exponential Calculations with Software 218 Exercises Section 6.3 (37–50) 218 6.4 Other Continuous Distributions 220 The Weibull Distribution 220 The Lognormal Distribution 222 The Beta Distribution 224 Exercises Section 6.4 (51–66) 226 6.5 Probability Plots 228 Sample Percentiles 228 A Probability Plot 229 Departures from Normality 232 Beyond Normality 234 Probability Plots in Matlab and R 236 Exercises Section 6.5 (67–76) 237 Supplementary Exercises (77–96) 238 7 Joint Probability Distributions 242 Introduction 242 7.1 Joint Distributions for Discrete Random Variables 242 The Joint Probability Mass Function for Two Discrete Random Variables 242 Marginal Probability Mass Functions 244 Independent Random Variables 245 More Than Two Random Variables 246 Exercises Section 7.1 (1–12) 248 7.2 Joint Distributions for Continuous Random Variables 250 The Joint Probability Density Function for Two Continuous Random Variables 250 Marginal Probability Density Functions 252 Independence of Continuous Random Variables 254 More Than Two Random Variables 255 Exercises Section 7.2 (13–22) 257 7.3 Expected Values Covariance and Correlation 258 Properties of Expected Value 260 Covariance 261 Correlation 263 Correlation Versus Causation 265 Exercises Section 7.3 (23–42) 266 7.4 Properties of Linear Combinations 267 Expected Value and Variance of a Linear Combination 268 The PDF of a Sum 271 Moment Generating Functions of Linear Combinations 273 Exercises Section 7.4 (43–65) 275 7.5 The Central Limit Theorem and the Law of Large Numbers 278 Random Samples 278 The Central Limit Theorem 282 A More General Central Limit Theorem 286 Other Applications of the Central Limit Theorem 287 The Law of Large Numbers 288 Proof of the Central Limit Theorem 290 Exercises Section 7.5 (66–82) 290 7.6 Simulation of Joint Probability Distributions 293 Simulating Values from a Joint PMF 293 Simulating Values from a Joint PDF 295 Exercises Section 7.6 (83–90) 297 Supplementary Exercises (91–124) 298 8 Joint Probability Distributions:additional Topics 304 Introduction 304 8.1 Conditional Distributions and Expectation 304 Conditional Distributions and Independence 306 Conditional Expectation and Variance 307 The Laws of Total Expectation and Variance 308 Exercises Section 8.1 (1–18) 313 8.2 The Bivariate Normal Distribution 315 Conditional Distributions of X and Y 317 Regression to the Mean 318 The Multivariate Normal Distribution 319 Bivariate Normal Calculations with Software 319 Exercises Section 8.2 (19–30) 320 8.3 Transformations of Jointly Distributed Random Variables 321 The Joint Distribution of Two New Random Variables 322 The Distribution of a Single New RV 323 The Joint Distribution of More Than Two New Variables 325 Exercises Section 8.3 (31–38) 326 8.4 Reliability 327 The Reliability Function 327 Series and Parallel System Designs 329 Mean Time to Failure 331 The Hazard Function 332 Exercises Section 8.4 (39–50) 335 8.5 Order Statistics 337 The Distributions of Yn and Y1 337 The Distribution of the ith Order Statistic 339 The Joint Distribution of All n Order Statistics 340 Exercises Section 8.5 (51–60) 342 8.6 Further Simulation Tools for Jointly Distributed Random Variables 343 The Conditional Distribution Method of Simulation 343 Simulating a Bivariate Normal Distribution 344 Simulation Methods for Reliability 346 Exercises Section 8.6 (61–68) 347 Supplementary Exercises (69–82) 348 9 the Basics of Statistical Inference 351 Introduction 351 9.1 Point Estimation 351 Estimates and Estimators 352 Assessing Estimators: Accuracy and Precision 354 Exercises Section 9.1 (1–18) 357 9.2 Maximum Likelihood Estimation 360 Some Properties of MLEs 366 Exercises Section 9.2 (19–30) 367 9.3 Statistical Intervals 368 Constructing a Confidence Interval 369 Confidence Intervals for a Population Proportion 369 Confidence Intervals for a Population Mean 371 Further Comments on Statistical Intervals 375 Confidence Intervals with Software 375 Exercises Section 9.3 (31–48) 376 9.4 Hypothesis Tests 379 Hypotheses and Test Procedures 380 Hypothesis Testing for a Population Mean 381 Errors in Hypothesis Testing and the Power of a Test 385 Hypothesis Testing for a Population Proportion 388 Software for Hypothesis Test Calculations 389 Exercises Section 9.4 (49–71) 391 9.5 Bayesian Estimation 393 The Posterior Distribution of a Parameter 394 Inferences from the Posterior Distribution 397 Further Comments on Bayesian Inference 398 Exercises Section 9.5 (72–80) 399 9.6 Simulation-Based Inference 400 The Bootstrap Method 400 Interval Estimation Using the Bootstrap 402 Hypothesis Tests Using the Bootstrap 404 More on Simulation-Based Inference 405 Exercises Section 9.6 (81–90) 405 Supplementary Exercises (91–116) 407 10 Markov Chains 411 Introduction 411 10.1 Terminology and Basic Properties 411 The Markov Property 413 Exercises Section 10.1 (1–10) 416 10.2 The Transition Matrix and the Chapman–Kolmogorov Equations 418 The Transition Matrix 418 Computation of Multistep Transition Probabilities 419 Exercises Section 10.2 (11–22) 423 10.3 Specifying an Initial Distribution 426 A Fixed Initial State 428 Exercises Section 10.3 (23–30) 429 10.4 Regular Markov Chains and the Steady-State Theorem 430 Regular Chains 431 The Steady-State Theorem 432 Interpreting the Steady-State Distribution 433 Efficient Computation of Steady-State Probabilities 435 Irreducible and Periodic Chains 437 Exercises Section 10.4 (31–43) 438 10.5 Markov Chains with Absorbing States 440 Time to Absorption 441 Mean Time to Absorption 444 Mean First Passage Times 448 Probabilities of Eventual Absorption 449 Exercises Section 10.5 (44–58) 451 10.6 Simulation of Markov Chains 453 Exercises Section 10.6 (59–66) 459 Supplementary Exercises (67–82) 461 11 Random Processes 465 Introduction 465 11.1 Types of Random Processes 465 Classification of Processes 468 Random Processes and Their Associated Random Variables 469 Exercises Section 11.1 (1–10) 470 11.2 Properties of the Ensemble: Mean and Autocorrelation Functions 471 Mean and Variance Functions 471 Autocovariance and Autocorrelation Functions 475 The Joint Distribution of Two Random Processes 477 Exercises Section 11.2 (11–24) 478 11.3 Stationary and Wide-Sense Stationary Processes 479 Properties of WSS Processes 483 Ergodic Processes 486 Exercises Section 11.3 (25–40) 488 11.4 Discrete-Time Random Processes 489 Special Discrete Sequences 491 Exercises Section 11.4 (41–52) 493 Supplementary Exercises (53–64) 494 12 Families of Random Processes 497 Introduction 497 12.1 Poisson Processes 497 Relation to Exponential and Gamma Distributions 499 Combining and Decomposing Poisson Processes 502 Alternative Definition of a Poisson Process 504 Nonhomogeneous Poisson Processes 505 The Poisson Telegraphic Process 506 Exercises Section 12.1 (1–18) 507 12.2 Gaussian Processes 509 Brownian Motion 510 Brownian Motion as a Limit 512 Further Properties of Brownian Motion 512 Variations on Brownian Motion 514 Exercises Section 12.2 (19–28) 515 12.3 Continuous-Time Markov Chains 516 Infinitesimal Parameters and Instantaneous Transition Rates 518 Sojourn Times and Transitions 520 Long-Run Behavior of Continuous-Time Markov Chains 523 Explicit Form of the Transition Matrix 526 Exercises Section 12.3 (29–40) 527 Supplementary Exercises (41–51) 529 13 Introduction to Signal Processing 532 Introduction 532 13.1 Power Spectral Density 532 Expected Power and the Power Spectral Density 532 Properties of the Power Spectral Density 535 Power in a Frequency Band 538 White Noise Processes 539 Cross-Power Spectral Density for Two Processes 541 Exercises Section 13.1 (1–21) 542 13.2 Random Processes and LTI Systems 544 Properties of the LTI System Output 545 Ideal Filters 548 Signal Plus Noise 551 Exercises Section 13.2 (22–38) 554 13.3 Discrete-Time Signal Processing 556 Random Sequences and LTI Systems 558 Sampling Random Sequences 560 Exercises Section 13.3 (39–50) 562 A Statistical Tables A- 1 A. 1 Binomial CDF A- 1 A. 2 Poisson CDF A- 4 A. 3 Standard Normal CDF A- 5 A. 4 Incomplete Gamma Function A- 7 A. 5 Critical Values for t Distributions A- 7 A. 6 Tail Areas of t Distributions A- 9 B Background Mathematics A- 13 B. 1 Trigonometric Identities A- 13 B. 2 Special Engineering Functions A- 13 B. 3 o(h) Notation A- 14 B. 4 The Delta Function A- 14 B. 5 Fourier Transforms A- 15 B. 6 Discrete-Time Fourier Transforms A- 16 C Important Probability Distributions A- 18 C. 1 Discrete Distributions A- 18 C. 2 Continuous Distributions A- 20 C. 3 Matlab and R Commands A- 23 Bibliography B- 1 Answers to Odd-numbered Exercises S- 1 Index I- 1

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Book SynopsisTable of ContentsPreface iv 1 Introduction to Statistics and Business Analytics 1 2 Visualizing Data with Charts and Graphs 22 3 Descriptive Statistics 57 4 Probability 93 5 Discrete Distributions 134 6 Continuous Distributions 172 7 Sampling and Sampling Distributions 208 8 Statistical Inference: Estimation for Single Populations 239 9 Statistical Inference: Hypothesis Testing for Single Populations 273 10 Statistical Inferences About Two Populations 323 11 Analysis of Variance and Design of Experiments 378 12 Simple Regression Analysis and Correlation 435 13 Multiple Regression Analysis 486 14 Building Multiple Regression Models 514 15 Time-Series Forecasting and Index Numbers 563 16 Analysis of Categorical Data 618 17 Nonparametric Statistics 638 18 Statistical Quality Control 684 19 Decision Analysis 727 Appendix A Tables 761 Glossary 802 Index 809

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Book SynopsisTHE STATISTICAL SLEUTH: A COURSE IN METHODS OF DATA ANALYSIS, Third Edition offers an appealing treatment of general statistical methods that takes full advantage of the computer, both as a computational and an analytical tool. The material is independent of any specific software package, and prominently treats modeling and interpretation in a way that goes beyond routine patterns. The book focuses on a serious analysis of real case studies, strategies and tools of modern statistical data analysis, the interplay of statistics and scientific learning, and the communication of results. With interesting examples, real data, and a variety of exercise types (conceptual, computational, and data problems), the authors get readers excited about statistics.Table of Contents1. Drawing Statistical Conclusions. 2. Inference Using t-Distributions. 3. A Closer Look at Assumptions. 4. Alternatives to the t-Tools. 5. Comparisons among Several Samples. 6. Linear Combinations and Multiple Comparisons of Means. 7. Simple Linear Regression: A Model for the Mean. 8. A Closer Look at Assumptions for Simple Linear Regression. 9. Multiple Regression. 10. Inferential Tools for Multiple Regression. 11. Model Checking and Refinement. 12. Strategies for Variable Selection. 13. The Analysis of Variance for Two-Way Classifications. 14. Multifactor Studies Without Replication. 15. Adjustment for Serial Correlation. 16. Repeated Measures and Other Multivariate Responses. 17. Exploratory Tools for Summarizing Multivariate Responses. 18. Comparisons of Proportions or Odds. 19. More Tools for Tables of Counts. 20. Logistics Regression for Binary Response Variables. 21. Logistic Regression for Binomial Counts. 22. Log-Linear Regression for Poisson Counts. 23. Elements of Research Design. 24. Factorial Treatment Arrangements and Blocking Designs. Appendix A. Tables. Appendix B. References. Bibliography. Index.

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Book SynopsisPRESTATISTICS gives you the skills you need to be successful in statistics, whether you are just out of high school or haven't taken a mathematics course in years. Each section in PRESTATISTICS concludes with a paragraph titled "Why We Learned It" that shows you the connection between the topics learned in that section and statistics--and how it will be helpful to you in an introductory statistics course. Nine hundred videos including lectures, example solutions and quick-check exercise walkthroughs enable you to learn the way you want to learn, and WebAssign--a flexible and fully customizable online solution available with this text--empowers you to prepare for class with confidenceTable of Contents1. Arithmetic Operations used in Statistics. Rounding Numbers. Types of Numbers and the Number Line. Fractions, Decimals and Percentages. Operations with Fractions. Absolute, Relative and Percent Error. Scientific Notation and E-Notation. Read and Use Mathematical Tables. 2. Algebraic Expressions used in Statistics and Basics of Solving Equations. Translating English into Algebra: Expressions, Equations and Inequalities. Order of Operations and Evaluating Numerical Expressions. Basics of Solving Linear Equations. 3. Equations, Inequalities and Problem-Solving Techniques. Solving Equations used in Statistics. Inequalities, Interval Notation and Plus/Minus Notation. Solving Absolute Value Inequalities. Introduction to Problem Solving. Literal Equations. 4. Graphing Linear Equations in Two Variables. Properties of Rectangular Coordinate System. Interpretation of Graphs. Graphing Linear Equations. Slope and Marginal Change. Equations of Lines in Statistics. 5. Sets, Counting and Sums. Fundamentals of Sets. Cardinality of Sets. Principles of Counting. Writing and Computing Sums. 6. Functions and Area Under Functions. Introduction to Functions. Linear and Piecewise Defined Functions. Area Under a Constant Function. Area Under a Linear Function. 7. Survey of Functions used in Statistics. Exponential and Logarithmic Functions. Rational Exponent and Power Functions. Multivariable Linear Functions.

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Book SynopsisExplains the mathematical underpinnings of baseball so that students can understand the world of statistics and probability. This book teaches fundamentals of probability and statistics through the feats of baseball legends such as Hank Aaron, Joe DiMaggio, and Ted Williams and more recent players Barry Bonds, Albert Pujols, and Alex Rodriguez.Trade ReviewSandlot Stats served as an instrumental and informative piece to the Baseball Statistics course. The amount of time and tedious effort put into the project is evident, as this book is absolutely packed with information. The book puts a new spin on mathematics, and makes it more understandable for even the most casual of baseball fans. Baseball purists and sabermetric geeks alike will love this book. -- Jon Alba Sports Paws Dr. Rothman has hit a 'home run.' Sandlot Stats: Learning Statistics with Baseball is not only a fine book to read, but a text which can also serve as an excellent resource book. -- Father Gabe Costa CBS New York For those interested in this subject-this is your book. -- Harvey Frommer Epoch Times If this had been the textbook for a basic statistics course that I took as a student, I might have remembered that course forever as the best class I ever had. -- Charles Ashbacher MAA Reviews Sandlot Stats is a readable and resourceful introductory textbook for statistics. -- Graham Wheeler Significance The book is very readable and well organized... High school statistics teachers could use this book as a course supplement or an enrichment source for sports-crazy students. Any college professor teaching a sports statistics course or looking for ways to enliven a traditional course would also find it interesting. Even baseball fans wanting to learn more about descriptive measures used in the game could benefit from Rothman's interesting exposition. -- Marc Michael Mathematics TeacherTable of ContentsAcknowledgmentsList of AbbreviationsIntroduction1. Basic Statistical Definitions2. Descriptive Statistics for One Quantitative Variable3. Descriptive Measures Used in Baseball4. Comparing Two Quantitative Data Sets5. Linear Regression and Correlation Analysis for Two Quantitative Variables6. Descriptive Statistics Applied to Qualitative Variables7. Probability8. Sports Betting9. Baseball and Traditional Descriptive Measures10. Final Comparison of Batting Performance between Aaron and Bonds11. Probability Distribution Functions for a Discrete Random Variable12. Probability Density Functions for a Continuous Variable13. Sampling Distributions14. Confidence Intervals15. Hypothesis Testing for One Population16. Streaking17. Mission Impossible: Batting .400 for a Season18. PostseasonAppendix A: Hypothesis Testing for Two Population ProportionsAppendix B: The Chi-Square DistributionAppendix C: Statistical TablesIndex

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