Mathematics Books

Book SynopsisSolutions Manual to AccompanyTable of ContentsPreface vii 1 First Ideas 1 1.1 Two Partial Differential Equations 1 1.2 Fourier Series 4 1.3 Two Eigenvalue Problems 12 1.4 A Proof of the Convergence Theorem 14 2 Solutions of the Heat Equation 15 2.1 Solutions on an Interval [0, L] 15 2.2 A Nonhomogeneous Problem 19 3 Solutions of the Wave Equation 25 3.1 Solutions on Bounded Intervals 25 3.2 The Cauchy Problem 32 3.2.1 d’Alembert’s Solution 32 3.2.2 The Cauchy Problem on a Half Line 36 3.2.3 Characteristic Triangles and Quadrilaterals 41 3.2.4 A Cauchy Problem with a Forcing Term 41 3.2.5 String with Moving Ends 42 3.3 The Wave Equation in Higher Dimensions 46 3.3.1 Vibrations in a Membrane with Fixed Frame 46 3.3.2 The Poisson Integral Solution 47 3.3.3 Hadamard’s Method of Descent 47 4 Dirichlet and Neumann Problems 49 4.1 Laplace’s Equation and Harmonic Functions 49 4.2 The Dirichlet Problem for a Rectangle 50 4.3 The Dirichlet Problem for a Disk 52 4.4 Properties of Harmonic Functions 57 4.4.1 Topology of Rn 57 4.4.2 Representation Theorems 58 4.4.3 The Mean Value Theorem and the Maximum Principle 60 4.5 The Neumann Problem 61 4.5.1 Uniqueness and Existence 61 4.5.2 Neumann Problem for a Rectangle 62 4.5.3 Neumann Problem for a Disk 63 4.6 Poisson’s Equation 64 4.7 An Existence Theorem for the Dirichlet Problem 65 5 Fourier Integral Methods of Solution 67 5.1 The Fourier Integral of a Function 67 5.2 The Heat Equation on the Real Line 70 5.3 The Debate Over the Age of the Earth 73 5.4 Burgers’ Equation 73 5.5 The Cauchy Problem for the Wave Equation 74 5.6 Laplace’s Equation on Unbounded Domains 76 6 Solutions Using Eigenfunction Expansions 79 6.1 A Theory of Eigenfunction Expansions 79 6.2 Bessel Functions 83 6.3 Applications of Bessel Functions 87 6.3.1 Temperature Distribution in a Solid Cylinder 87 6.3.2 Vibrations of a Circular Drum 87 6.4 Legendre Polynomials and Applications 90 7 Integral Transform Methods of Solution 97 7.1 The Fourier Transform 97 7.2 Heat and Wave Equations 101 7.3 The Telegraph Equation 104 7.4 The Laplace Transform 106 8 First-Order Equations 109 8.1 Linear First-Order Equations 109 8.2 The Significance of Characteristics 111 8.3 The Quasi-Linear Equation 114 Series List 117

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Book SynopsisPraise for the First Edition . this book is quite inspiring, giving many practical ideas for survey research, especially for designing better questionnaires.Table of ContentsPreface to the Second Edition xiii Preface xv Acknowledgments xvii Introduction 1 I.1 Designing a Survey 4 I.1.1 Choice of a Topic 4 I.1.2 Choice of the Most Important Variables 4 I.1.3 Choice of a Data Collection Method 5 I.1.4 Choice of Operationalization 6 I.1.5 Test of the Quality of the Questionnaire 8 I.1.6 Formulation of the Final Questionnaire 9 I.1.7 Choice of Population and Sample Design 9 I.1.8 Decide about the Fieldwork 10 I.1.9 What We Know about These Decisions 10 I.1.10 Summary 11 Exercises 12 Part I The Three-Step Procedure to Design Requests for Answers 13 1 Concepts-by-Postulation and Concepts-by-Intuition 15 1.1 Concepts-by-Intuition and Concepts-by-Postulation 15 1.2 Different Ways of Defining Concepts-by-Postulation through Concepts-by-Intuition 19 1.2.1 Job Satisfaction as a Concept-by-Intuition 19 1.2.2 Job Satisfaction as a Concept-by-Postulation 20 1.3 Summary 27 Exercises 28 2 From Social Science Concepts-by-Intuition to Assertions 30 2.1 Basic Concepts and Concepts-by-Intuition 31 2.2 Assertions and Requests for an Answer 32 2.3 The Basic Elements of Assertions 33 2.3.1 Indirect Objects as Extensions of Simple Assertions 36 2.3.2 Adverbials as Extensions of Simple Assertions 37 2.3.3 Modifiers as Extensions of Simple Assertions 37 2.3.4 Object Complements as Extensions of Simple Assertions 38 2.3.5 Some Notation Rules 38 2.4 Basic Concepts-by-Intuition 39 2.4.1 Subjective Variables 40 2.4.2 Objective Variables 47 2.4.3 In Summary 49 2.5 Alternative Formulations for the Same Concept 49 2.6 Extensions of Simple Sentences 51 2.6.1 Adding Indirect Objects 51 2.6.2 Adding Modifiers 52 2.6.3 Adding Adverbials 52 2.7 Use of Complex Sentences 53 2.7.1 Complex Sentences with No Shift in Concept 54 2.7.2 Complex Sentences with a Shift in Concept 54 2.7.3 Adding Conditions to Complex Sentences 56 2.8 Summary 56 Exercises 57 3 The Formulation of Requests for an Answer 60 3.1 From Concepts to Requests for an Answer 61 3.2 Different Types of Requests for an Answer 63 3.2.1 Direct Request 63 3.2.2 Indirect Request 66 3.3 The Meaning of Requests for an Answer with WH Request Words 69 3.3.1 “When,” “Where,” and “Why” Requests 70 3.3.2 “Who” Requests 70 3.3.3 “Which” Requests 70 3.3.4 “What” Requests 71 3.3.5 “How” Requests 72 3.4 Summary 74 Exercises 75 Part II Choices Involved in Questionnaire Design 77 4 Specific Survey Research Features of Requests for an Answer 79 4.1 Select Requests from Databases 79 4.2 Other Features Connected with the Research Goal 81 4.3 Some Problematic Requests 83 4.3.1 Double-Barreled Requests 83 4.3.2 Requests with Implicit Assumptions 84 4.4 Some Prerequests Change the Concept-by-Intuition 85 4.5 Batteries of Requests for Answers 86 4.5.1 The Use of Batteries of Stimuli 87 4.5.2 The Use of Batteries of Statements 88 4.6 Other Features of Survey Requests 92 4.6.1 The Formulation of Comparative or Absolute Requests for Answers 92 4.6.2 Conditional Clauses Specified in Requests for Answers 93 4.6.3 Balanced or Unbalanced Requests for Answers 93 4.7 Special Components within the Request 95 4.7.1 Requests for Answers with Stimulation for an Answer 95 4.7.2 Emphasizing the Subjective Opinion of the Respondent 95 4.8 Summary 96 Exercises 96 5 Response Alternatives 98 5.1 Open Requests for an Answer 99 5.2 Closed Categorical Requests 101 5.2.1 Nominal Categories 103 5.2.2 Ordinal Scales 104 5.2.3 Continuous Scales 108 5.3 How Many Categories are Optimal? 111 5.4 Summary 112 Exercises 114 6 The Structure of Open-Ended and Closed Survey Items 115 6.1 Description of the Components of Survey Items 115 6.2 Different Structures of Survey Items 118 6.2.1 Open-Ended Requests for an Answer 119 6.2.2 Closed Survey Items 120 6.2.3 The Frequency of Occurrence 124 6.2.4 The Complexity of Survey Items 125 6.3 What Form of Survey Items Should Be Recommended? 126 6.4 Summary 127 Exercises 128 7 Survey Items in Batteries 130 7.1 Batteries in Oral Interviews 131 7.2 Batteries in Mail Surveys 134 7.3 Batteries in CASI 138 7.4 Summary and Discussion 142 Exercises 144 8 Mode of Data Collection and Other Choices 146 8.1 The Choice of the Mode of Data Collection 147 8.1.1 Relevant Characteristics of the Different Modes 148 8.1.2 The Presence of the Interviewer 149 8.1.3 The Mode of Presentation 151 8.1.4 The Role of the Computer 152 8.1.5 Procedures without Asking Questions 155 8.1.6 Mixed-Mode Data Collection 155 8.2 The Position in the Questionnaire 156 8.3 The Layout of the Questionnaire 158 8.4 Differences due to Use of Different Languages 158 8.5 Summary and Discussion 159 Exercises 160 Part III Estimation and Prediction of the Quality of Questions 163 9 Criteria for the Quality of Survey Measures 165 9.1 Different Methods, Different Results 166 9.2 How These Differences Can Be Explained 173 9.2.1 Specifications of Relationships between Variables in General 173 9.2.2 Specification of Measurement Models 175 9.3 Quality Criteria for Survey Measures and Their Consequences 178 9.4 Alternative Criteria for Data Quality 181 9.4.1 Test–Retest Reliability 181 9.4.2 The Quasi-simplex Approach 182 9.4.3 Correlations with Other Variables 183 9.5 Summary and Discussion 184 Exercises 185 Appendix 9.1 The Specification of Structural Equation Models 187 10 Estimation of Reliability, Validity, and Method Effects 190 10.1 Identification of the Parameters of a Measurement Model 191 10.2 Estimation of Parameters of Models with Unmeasured Variables 195 10.3 Estimating Reliability, Validity, and Method Effects 197 10.4 Summary and Discussion 201 Exercises 202 Appendix 10.1 Input of Lisrel for Data Analysis of a Classic MTMM Study 205 Appendix 10.2 Relationship between the TS and the Classic MTMM Model 205 11 Split-Ballot Multitrait–Multimethod Designs 208 11.1 The Split-Ballot MTMM Design 209 11.1.1 The Two-Group Design 209 11.1.2 The Three-Group Design 210 11.1.3 Other SB-MTMM Designs 211 11.2 Estimating and Testing Models for Split-Ballot MTMM Experiments 212 11.3 Empirical Examples 213 11.3.1 Results for the Three-Group Design 213 11.3.2 Two-Group SB-MTMM Design 215 11.4 The Empirical Identifiability and Efficiency of the Different SB-MTMM Designs 218 11.4.1 The Empirical Identifiability of the SB-MTMM Model 218 11.4.2 The Efficiency of the Different Designs 221 11.5 Summary and Discussion 221 Exercises 222 Appendix 11.1 The Lisrel Input for the Three-Group SB-MTMM Example 222 12 MTMM Experiments and the Quality of Survey Questions 225 12.1 The Data from the MTMM Experiments 226 12.2 The Coding of the Characteristics of the MTMM Questions 229 12.3 The Database and Some Results 230 12.3.1 Differences in Quality across Countries 231 12.3.2 Differences in Quality for Domains and Concepts 234 12.3.3 Effect of the Question Formulation on the Quality 235 12.4 Prediction of the Quality of Questions Not Included in the MTMM Experiments 237 12.4.1 Suggestions for Improvement of Questions 239 12.4.2 Evaluation of the Quality of the Prediction Models 240 12.5 Summary 241 Exercises 242 Part IV Applications in Social Science Research 243 13 The SQP 2.0 Program for Prediction of Quality and Improvement of Measures 245 13.1 The Quality of Questions Involved in the MTMM Experiments 246 13.1.1 The Quality of Specific Questions 246 13.1.2 Looking for Optimal Measures for a Concept 250 13.2 The Quality of Non-MTMM Questions in the Database 252 13.3 Predicting the Quality of New Questions 256 13.4 Summary 261 Exercises 262 14 The Quality of Measures for Concepts-by-Postulation 263 14.1 The Structures of Concepts-by-Postulation 264 14.2 The Quality of Measures of Concepts-by-Postulation with Reflective Indicators 264 14.2.1 Testing the Models 265 14.2.2 Estimation of the Composite Scores 268 14.2.3 The Quality of Measures for Concepts-by-Postulation 270 14.2.4 Improvement of the Quality of the Measure 274 14.3 The Quality of Measures for Concepts-by-Postulation with Formative Indicators 276 14.3.1 Testing the Models 278 14.3.2 Estimation of the Composite Score 281 14.3.3 The Estimation of the Quality of the Composite Scores 282 14.4 Summary 283 Exercises 284 Appendix 14.1 Lisrel Input for Final Analysis of the Effect of “Social Contact” on “Happiness” 284 Appendix 14.2 Lisrel Input for Final Analysis of the Effect of “Interest in Political Issues in the Media” on “Political Interest in General” 285 15 Correction for Measurement Errors 287 15.1 Correction for Measurement Errors in Models with only Concepts-by-Intuition 287 15.2 Correction for Measurement Errors in Models with Concepts-by-Postulation 292 15.2.1 Operationalization of the Concepts 292 15.2.2 The Quality of the Measures 294 15.2.3 Correction for Measurement Errors in the Analysis 297 15.3 Summary 298 Exercises 299 Appendix 15.1 Lisrel Inputs to Estimate the Parameters of the Model in Figure 15.1 300 Appendix 15.2 Lisrel Input for Estimation of the Model with Correction for Measurement Errors using Variance Reduction by Quality for all Composite Scores 301 16 Coping with Measurement Errors in Cross-Cultural Research 302 16.1 Notations of Response Models for Cross-Cultural Comparisons 303 16.2 Testing for Equivalence or Invariance of Instruments 307 16.2.1 The Standard Approach to Test for Equivalence 307 16.3 Problems Related with the Procedure 309 16.3.1 Using Information about the Power of the Test 309 16.3.2 An Alternative Test for Equivalence 315 16.3.3 The Difference between Significance and Relevance 317 16.4 Comparison of Means and Relationships across Groups 318 16.4.1 Comparison of Means and Relationships between Single Requests for Answers 318 16.4.2 Comparison of Means and Relationships Based on Composite Scores 319 16.4.3 Comparison of Means and Relationships between Latent Variables 321 16.5 Summary 324 Exercises 325 Appendix 16.1 The Two Sets of Requests Concerning “Subjective Competence” 326 Appendix 16.2 ESS Requests Concerning “Political Trust” 327 Appendix 16.3 The Standard Test of Equivalence for “Subjective Competence” 328 Appendix 16.4 The Alternative Equivalence Test for “Subjective Competence” in Three Countries 329 Appendix 16.5 Lisrel Input to Estimate the Null Model for Estimation of the Relationship between “Subjective Competence” and “Political Trust” 331 Appendix 16.6 Derivation of the Covariance between the Composite Scores 333 References 336 Index 352

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Book SynopsisHIGHLIGHTS THE USE OF BAYESIAN STATISTICS TO GAIN INSIGHTS FROM EMPIRICAL DATA Featuring an accessible approach, Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems demonstrates how Bayesian statistics can help to provide insights into important issues facing business and management. The book draws on multidisciplinary applications and examples and utilizes the freely available software WinBUGS and R to illustrate the integration of Bayesian statistics within data-rich environments. Computational issues are discussed and integrated with coverage of linear models, sensitivity analysis, Markov Chain Monte Carlo (MCMC), and model comparison. In addition, more advanced models including hierarchal models, generalized linear models, and latent variable models are presented to further bridge the theory and application in real-world usage. Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems alTable of ContentsPreface xv 1 Introduction to Bayesian Methods 1 1.1 Bayesian Methods: An Aerial Survey 1 1.1.1 Informal Example 3 1.2 Bayes’ Theorem 4 1.3 Bayes’ Theorem and the Focus Group 6 1.4 The Flavors of Probability 8 1.4.1 Common Ground 9 1.4.2 Frequency-Based Probability 9 1.4.3 Subjective Probability 10 1.5 Summary 11 1.6 Notation Introduced in this Chapter 11 2 A First Look at Bayesian Computation 12 2.1 Getting Started 12 2.2 Selecting the Likelihood Function 13 2.3 Selecting the Functional Form 16 2.4 Selecting the Prior 17 2.5 Finding the Normalizing Constant 18 2.6 Obtaining the Posterior 19 2.7 Communicating Findings 23 2.8 Predicting Future Outcomes 26 2.9 Summary 28 2.10 Exercises 28 2.11 Notation Introduced in this Chapter 29 3 Computer-Assisted Bayesian Computation 30 3.1 Getting Started 30 3.2 Random Number Sequences 31 3.3 Monte Carlo Integration 33 3.4 Monte Carlo Simulation for Inference 36 3.4.1 Testing for a Difference in Proportions 37 3.4.2 Predicting Customer Behavior 38 3.4.3 Predicting Customer Behavior Part 2 40 3.5 The Conjugate Normal Model 40 3.5.1 The Conjugate Normal Model: Mean with Variance Known 40 3.5.2 The Conjugate Normal Model: Variance with Mean Known 42 3.5.3 The Conjugate Normal Model with Mean and Variance Both Unknown 44 3.6 In Practice: Inference for the Conjugate Normal Model 45 3.6.1 Conjugate Normal Mean with Variance Known 46 3.6.2 Conjugate Normal Variance with Mean Known 47 3.6.3 Conjugate Normal Mean and Variance Both Unknown 48 3.7 Count Data and the Conjugate Poisson Model 52 3.7.1 In Detail: Conjugate Poisson Model Development 53 3.7.2 In Practice: Inference for the Conjugate Poisson Model 54 3.8 Summary 56 3.9 Exercises 56 3.10 Notation Introduced in this Chapter 58 3.11 Appendix—In Detail: Finding Posterior Distributions for the Normal Model 58 3.11.1 Analysis of the Normal Mean with Variance Known 59 3.11.2 Analysis of the Normal Variance with Mean Known 61 3.11.3 Analysis of the Conjugate Normal Model with Mean and Variance Both Unknown 62 4 Markov Chain Monte Carlo and Regression Models 64 4.1 Introduction to Markov Chain Monte Carlo 64 4.2 Fundamentals of MCMC 66 4.3 Gibbs Sampling 67 4.3.1 Gibbs Sampling for the Normal Mean 69 4.3.2 Output Analysis 70 4.4 Gibbs Sampling and the Simple Linear Regression Model 73 4.5 In Practice: The Simple Linear Regression Model 76 4.6 The Metropolis Algorithm 79 4.6.1 In Practice: Simulating from a Standard Normal Distribution Using the Metropolis Algorithm 81 4.6.2 In Practice: Regression Analysis Using the Metropolis Algorithm 85 4.7 Hastings’ Extension of the Metropolis Algorithm 87 4.7.1 In Practice: The Metropolis–Hastings Algorithm 89 4.7.2 The Relationship Between the Gibbs Sampler and the Metropolis–Hastings Algorithm 90 4.8 Summary 91 4.9 Exercises 92 5 Estimating Bayesian Models With WinBUGS 93 5.1 An Introduction to WinBUGS 94 5.2 In Practice: A First WinBUGS Model 95 5.3 In Practice: Models for the Mean in WinBUGS 104 5.3.1 Examining the Single-Sample Mean 104 5.3.2 The Two-Sample t-Test 106 5.3.3 An Alternative Parameterization of the Two-Sample t-Test 108 5.4 Examining the Prior’s Influence with Sensitivity Analysis 111 5.4.1 Sensitivity Analysis with Informative Priors 111 5.4.2 Sensitivity Analysis with Noninformative Priors 113 5.4.3 In Practice: Pre-sensitivity Analysis: Graphically Examining a Mean Parameter’s Prior and Posterior Distribution 114 5.4.4 In Practice: Pre-sensitivity Analysis—Graphically Examining a Precision Parameter 117 5.4.5 In Practice: Sensitivity Analysis for a Mean Parameter 118 5.4.6 In Practice: Sensitivity Analysis for a Precision Parameter 118 5.5 In Practice: Examining Proportions in WinBUGS 120 5.5.1 Analyzing Differences in Proportions 121 5.5.2 Predicting Customer Behavior: Part 2 Revisited 124 5.6 Analysis of Variance Models 125 5.6.1 In Practice: One-Way ANOVA 126 5.6.2 In Practice: One-Way ANOVA with Effects Coding 132 5.6.3 In Practice: One-Way ANOVA with Unequal Variances 133 5.6.4 Indexing Parameters by Group Membership Variables 136 5.7 Higher Order ANOVA Models 137 5.7.1 In Practice: Two-Way ANOVA with structure Data 139 5.7.2 Two-Way ANOVA with Group Indicator Variables 140 5.7.3 Using Columnar Data in WinBUGS 143 5.8 Regression and ANCOVA Models in WinBUGS 144 5.8.1 In Practice: Simple Linear Regression Using WinBUGS 145 5.8.2 In Practice: ANCOVA Models Using WinBUGS 147 5.8.3 In Practice: “Undifferenced” ANCOVA Models Using WinBUGS 150 5.9 Summary 152 5.10 Chapter Appendix: Exporting WinBUGS MCMC Output to R 152 5.11 Exercises 153 6 Assessing MCMC Performance inWinBUGS 155 6.1 Convergence Issues in MCMC Modeling 155 6.2 Output Diagnostics in WinBUGS 158 6.2.1 The Quantiles Tool 158 6.2.2 The Autocorrelation Function Tool 159 6.3 Reparameterizing to Improve Convergence 161 6.4 Number and Length of Chains 165 6.4.1 Number of Chains 165 6.4.2 Length of Chains 173 6.5 Metropolis–Hastings Acceptance Rates 175 6.6 Summary 177 6.7 Exercises 178 7 Model Checking and Model Comparison 180 7.1 Graphical Model Checking 180 7.1.1 In Practice: Graphical Fit Plots 181 7.1.2 In Practice: Residual Analysis 183 7.2 Predictive Densities and Checking Model Assumptions 185 7.2.1 The Posterior Predictive p-value 186 7.2.2 In Detail: Comparing Posterior Predictive p-Value Test Statistics 190 7.3 Variable Selection Methods 192 7.3.1 Kuo and Mallick’s Method 192 7.3.2 In Practice: Kuo and Mallick Variable Selection 194 7.3.3 Gibbs Variable Selection 196 7.3.4 In Practice: Gibbs Variable Selection 197 7.3.5 Reversible Jump MCMC 197 7.3.6 In Practice: Reversible Jump MCMC with WinBUGS 198 7.4 Bayes Factors and Bayesian Information Criterion 201 7.4.1 In Practice: Calculating the Marginal Likelihood for a Simple Proportion 204 7.4.2 Bayesian Information Criterion 205 7.5 Deviance Information Criterion 208 7.5.1 AIC and Classical Non-nested Model Selection 208 7.5.2 DIC: A Bayesian Version of AIC 209 7.5.3 In Practice: DIC for Variable Selection 211 7.5.4 In Practice: Likelihood Transformations and DIC 213 7.6 Summary 214 7.7 Exercises 214 8 Hierarchical Models 217 8.1 Fundamentals of Hierarchical Models 218 8.1.1 In Detail: Hierarchical Model Error Terms 222 8.1.2 In Practice: The One-Way Random-Effects ANOVA Model 223 8.1.3 In Practice: Hierarchical Centering 225 8.1.4 In Practice: Examining Alternative Priors for Variance Components 226 8.1.5 In Practice: Longitudinal Modeling 227 8.2 The Random Coefficients Model 228 8.2.1 In Practice: Structuring Data for Hierarchical Models 231 8.2.2 In Practice: The Random Coefficients Model 233 8.2.3 In Practice: Changing Random Coefficients to Be Non-random 236 8.2.4 In Practice: Multiple-Predictor Random Coefficients Models 237 8.3 Hierarchical Models for Variance Terms 238 8.4 Functional Forms at Multiple Hierarchical Levels 242 8.4.1 In Practice: Second-Level Functional Forms 245 8.4.2 In Practice: Interpreting Second-Level Coefficients 247 8.5 In Detail: Modeling Covarying Hierarchical Terms 249 8.5.1 Specifying Priors for the Bivariate Normal 250 8.5.2 In Practice: The Covarying Random Coefficients Model 252 8.5.3 In Practice: Case Studies in the Covarying Random Coefficients Model 254 8.6 Summary 256 8.7 Exercises 256 8.8 Notation Introduced in this Chapter 257 9 Generalized Linear Models 259 9.1 Fundamentals of Generalized Linear Models 259 9.2 Count Data Models: Poisson Regression 262 9.3 Models for Binary Data: Logistic Regression 266 9.4 The Probit Model 271 9.5 In Detail: Multinomial Logistic Regression for Categorical Outcomes 274 9.5.1 In Practice: Multinomial Logit for Contingency Tables 277 9.5.2 In Practice: Multinomial Logit with Continuous Predictors 279 9.6 Hierarchical Models for Count Data 281 9.6.1 The Negative Binomial Regression Model 282 9.6.2 In Practice: Simulating from the Negative Binomial Distribution 282 9.6.3 In Practice: Negative Binomial Regression 285 9.7 Hierarchical Models for Binary Data 287 9.7.1 In Practice: Logistic Regression with Random Intercepts 288 9.8 Summary 290 9.9 Exercises 291 9.10 Notation Introduced in this Chapter 292 10 Models For Difficult Data 294 10.1 Living with Outliers—Robust Regression Models 294 10.1.1 Another Look at the t-Distribution 296 10.1.2 In Practice: Robust Regression with the t-Distribution 297 10.1.3 In Detail: Placing a Prior on 301 10.2 Handling Heteroscedasticity by Modeling Variance Parameters 304 10.2.1 In Practice: Modeling Heteroscedasticity 305 10.3 Dealing with Missing Data 309 10.4 Types of Missing Data 311 10.4.1 Missing Completely at Random Data 311 10.4.2 In Practice: Analyzing MCAR Data 312 10.4.3 Missing at Random Data 314 10.4.4 In Practice: Analyzing MAR Data 315 10.4.5 Missing Not at Random Data 317 10.5 Missing Covariate Data and Non-Normal Missing Data 318 10.6 Summary 319 10.7 Exercises 320 10.8 Notation Introduced in this Chapter 321 11 Introduction To Latent Variable Models 322 11.1 Not Seen but Felt 322 11.2 Latent Variable Models for Binary Data 323 11.2.1 In Practice: The Probit Model Using Latent Variables 325 11.3 Structural Break Models 327 11.3.1 In Practice: Estimating Structural Break Models 329 11.3.2 In Practice: Adding Covariates to Structural Break Models 332 11.3.3 In Detail: Improving Parameter Mixing in Structural Break Models 333 11.4 In Detail: The Ordinal Probit Model 335 11.4.1 Posterior Simulation in the Ordinal Probit Model 336 11.4.2 In Practice: Modeling Credit Ratings with Ordinal Probit 339 11.5 Summary 341 11.6 Exercises 342 AppendixA Common Statistical Distributions 344 References 346 Author Index 357 Subject Index 361

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Book SynopsisA guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators.?The authors also include problem sets to enhance learning. This book is a volume in thTable of ContentsList of Figures xvii List of Tables xxi Preface xxvii Abbreviations and Acronyms xxxi List of Symbols xxxiii 1 Introduction to Ridge Regression 1 1.1 Introduction 1 1.1.1 Multicollinearity Problem 3 1.2 Ridge Regression Estimator: Ridge Notion 5 1.3 LSE vs. RRE 6 1.4 Estimation of Ridge Parameter 7 1.5 Preliminary Test and Stein-Type Ridge Estimators 8 1.6 High-Dimensional Setting 9 1.7 Notes and References 11 1.8 Organization of the Book 12 2 Location and Simple Linear Models 15 2.1 Introduction 15 2.2 Location Model 16 2.2.1 Location Model: Estimation 16 2.2.2 Shrinkage Estimation of Location 17 2.2.3 Ridge Regression–Type Estimation of Location Parameter 18 2.2.4 LASSO for Location Parameter 18 2.2.5 Bias and MSE Expression for the LASSO of Location Parameter 19 2.2.6 Preliminary Test Estimator, Bias, and MSE 23 2.2.7 Stein-Type Estimation of Location Parameter 24 2.2.8 Comparison of LSE, PTE, Ridge, SE, and LASSO 24 2.3 Simple Linear Model 26 2.3.1 Estimation of the Intercept and Slope Parameters 26 2.3.2 Test for Slope Parameter 27 2.3.3 PTE of the Intercept and Slope Parameters 27 2.3.4 Comparison of Bias and MSE Functions 29 2.3.5 Alternative PTE 31 2.3.6 Optimum Level of Significance of Preliminary Test 33 2.3.7 Ridge-Type Estimation of Intercept and Slope 34 2.3.7.1 Bias and MSE Expressions 35 2.3.8 LASSO Estimation of Intercept and Slope 36 2.4 Summary and Concluding Remarks 39 3 ANOVA Model 43 3.1 Introduction 43 3.2 Model, Estimation, and Tests 44 3.2.1 Estimation of Treatment Effects 45 3.2.2 Test of Significance 45 3.2.3 Penalty Estimators 46 3.2.4 Preliminary Test and Stein-Type Estimators 47 3.3 Bias and Weighted L2 Risks of Estimators 48 3.3.1 Hard Threshold Estimator (Subset Selection Rule) 48 3.3.2 LASSO Estimator 49 3.3.3 Ridge Regression Estimator 51 3.4 Comparison of Estimators 52 3.4.1 Comparison of LSE with RLSE 52 3.4.2 Comparison of LSE with PTE 52 3.4.3 Comparison of LSE with SE and PRSE 53 3.4.4 Comparison of LSE and RLSE with RRE 54 3.4.5 Comparison of RRE with PTE, SE, and PRSE 56 3.4.5.1 Comparison Between 𝜽n^RR (kopt) and 𝜽n^PT (𝛼) 56 3.4.5.2 Comparison Between 𝜽n^RR (kopt) and 𝜽n^ s 56 3.4.5.3 Comparison of 𝜽n^RR (kopt) with 𝜽n^S+ 57 3.4.6 Comparison of LASSO with LSE and RLSE 58 3.4.7 Comparison of LASSO with PTE, SE, and PRSE 59 3.4.8 Comparison of LASSO with RRE 60 3.5 Application 60 3.6 Efficiency in Terms of Unweighted L2 Risk 63 3.7 Summary and Concluding Remarks 72 3A. Appendix 74 4 Seemingly Unrelated Simple Linear Models 79 4.1 Model, Estimation, and Test of Hypothesis 79 4.1.1 LSE of 𝜃 and 𝛽 80 4.1.2 Penalty Estimation of 𝛽 and 𝜃 80 4.1.3 PTE and Stein-Type Estimators of 𝛽 and 𝜃 81 4.2 Bias and MSE Expressions of the Estimators 82 4.3 Comparison of Estimators 86 4.3.1 Comparison of LSE with RLSE 86 4.3.2 Comparison of LSE with PTE 86 4.3.3 Comparison of LSE with SE and PRSE 87 4.3.4 Comparison of LSE and RLSE with RRE 87 4.3.5 Comparison of RRE with PTE, SE, and PRSE 89 4.3.5.1 Comparison Between 𝜽n^RR (kopt) and 𝜽n^PT 89 4.3.5.2 Comparison Between 𝜽n^RR (kopt) and 𝜽n^S 89 4.3.5.3 Comparison of 𝜽n^RR (kopt) with 𝜽n^S+ 90 4.3.6 Comparison of LASSO with RRE 90 4.3.7 Comparison of LASSO with LSE and RLSE 92 4.3.8 Comparison of LASSO with PTE, SE, and PRSE 92 4.4 Efficiency in Terms of Unweighted L2 Risk 93 4.4.1 Efficiency for 𝜷 94 4.4.2 Efficiency for 𝜽 95 4.5 Summary and Concluding Remarks 96 5 Multiple Linear Regression Models 109 5.1 Introduction 109 5.2 Linear Model and the Estimators 110 5.2.1 Penalty Estimators 111 5.2.2 Shrinkage Estimators 113 5.3 Bias and Weighted L2 Risks of Estimators 114 5.3.1 Hard Threshold Estimator 114 5.3.2 Modified LASSO 116 5.3.3 Multivariate Normal Decision Theory and Oracles for Diagonal Linear Projection 117 5.3.4 Ridge Regression Estimator 119 5.3.5 Shrinkage Estimators 119 5.4 Comparison of Estimators 120 5.4.1 Comparison of LSE with RLSE 120 5.4.2 Comparison of LSE with PTE 121 5.4.3 Comparison of LSE with SE and PRSE 121 5.4.4 Comparison of LSE and RLSE with RRE 122 5.4.5 Comparison of RRE with PTE, SE, and PRSE 123 5.4.5.1 Comparison Between 𝜽n^RR (kopt) and 𝜽n^PT(𝛼) 123 5.4.5.2 Comparison Between 𝜽n^RR (kopt) and 𝜽n^S 124 5.4.5.3 Comparison of 𝜽n^RR (kopt) with 𝜽n^S+ 124 5.4.6 Comparison of MLASSO with LSE and RLSE 125 5.4.7 Comparison of MLASSO with PTE, SE, and PRSE 126 5.4.8 Comparison of MLASSO with RRE 127 5.5 Efficiency in Terms of Unweighted L2 Risk 127 5.6 Summary and Concluding Remarks 129 6 Ridge Regression in Theory and Applications 143 6.1 Multiple Linear Model Specification 143 6.1.1 Estimation of Regression Parameters 143 6.1.2 Test of Hypothesis for the Coefficients Vector 145 6.2 Ridge Regression Estimators (RREs) 146 6.3 Bias, MSE, and L2 Risk of Ridge Regression Estimator 147 6.4 Determination of the Tuning Parameters 151 6.5 Ridge Trace 151 6.6 Degrees of Freedom of RRE 154 6.7 Generalized Ridge Regression Estimators 155 6.8 LASSO and Adaptive Ridge Regression Estimators 156 6.9 Optimization Algorithm 158 6.9.1 Prostate Cancer Data 160 6.10 Estimation of Regression Parameters for Low-Dimensional Models 161 6.10.1 BLUE and Ridge Regression Estimators 161 6.10.2 Bias and L2-risk Expressions of Estimators 162 6.10.3 Comparison of the Estimators 165 6.10.4 Asymptotic Results of RRE 166 6.11 Summary and Concluding Remarks 168 7 Partially Linear Regression Models 171 7.1 Introduction 171 7.2 Partial Linear Model and Estimation 172 7.3 Ridge Estimators of Regression Parameter 174 7.4 Biases and L2 Risks of Shrinkage Estimators 177 7.5 Numerical Analysis 178 7.5.1 Example: Housing Prices Data 182 7.6 High-Dimensional PLM 188 7.6.1 Example: Riboflavin Data 192 7.7 Summary and Concluding Remarks 193 8 Logistic Regression Model 197 8.1 Introduction 197 8.1.1 Penalty Estimators 199 8.1.2 Shrinkage Estimators 200 8.1.3 Results on MLASSO 201 8.1.4 Results on PTE and Stein-Type Estimators 202 8.1.5 Results on Penalty Estimators 204 8.2 Asymptotic Distributional L2 Risk Efficiency Expressions of the Estimators 204 8.2.1 MLASSO vs. MLE 205 8.2.2 MLASSO vs. RMLE 206 8.2.3 Comparison of MLASSO vs. PTE 206 8.2.4 PT and MLE 207 8.2.5 Comparison of MLASSO vs. SE 208 8.2.6 Comparison of MLASSO vs. PRSE 208 8.2.7 RRE vs. MLE 209 8.2.7.1 RRE vs. RMLE 209 8.2.8 Comparison of RRE vs. PTE 211 8.2.9 Comparison of RRE vs. SE 211 8.2.10 Comparison of RRE vs. PRSE 212 8.2.11 PTE vs. SE and PRSE 212 8.2.12 Numerical Comparison Among the Estimators 213 8.3 Summary and Concluding Remarks 213 9 Regression Models with Autoregressive Errors 221 9.1 Introduction 221 9.1.1 Penalty Estimators 223 9.1.2 Shrinkage Estimators 224 9.1.2.1 Preliminary Test Estimator 224 9.1.2.2 Stein-Type and Positive-Rule Stein-Type Estimators 225 9.1.3 Results on Penalty Estimators 225 9.1.4 Results on PTE and Stein-Type Estimators 226 9.1.5 Results on Penalty Estimators 229 9.2 Asymptotic Distributional L2-risk Efficiency Comparison 230 9.2.1 Comparison of GLSE with RGLSE 230 9.2.2 Comparison of GLSE with PTE 231 9.2.3 Comparison of LSE with SE and PRSE 231 9.2.4 Comparison of LSE and RLSE with RRE 232 9.2.5 Comparison of RRE with PTE, SE and PRSE 233 9.2.5.1 Comparison Between 𝜷n^GRR(kopt) and 𝜷n^G(PT)233 9.2.5.2 Comparison Between 𝜷n^GRR(kopt) and 𝜷n^G(S) 234 9.2.5.3 Comparison of 𝜷n^GRR(kopt) with 𝜷n^G(S+) 234 9.2.6 Comparison of MLASSO with GLSE and RGLSE 235 9.2.7 Comparison of MLASSO with PTE, SE, and PRSE 236 9.2.8 Comparison of MLASSO with RRE 236 9.3 Example: Sea Level Rise at KeyWest, Florida 237 9.3.1 Estimation of the Model Parameters 237 9.3.1.1 Testing for Multicollinearity 237 9.3.1.2 Testing for Autoregressive Process 238 9.3.1.3 Estimation of Ridge Parameter k 239 9.3.2 Relative Efficiency 240 9.3.2.1 Relative Efficiency (REff) 240 9.3.2.2 Effect of Autocorrelation Coefficient 𝜙 243 9.4 Summary and Concluding Remarks 245 10 Rank-Based Shrinkage Estimation 251 10.1 Introduction 251 10.2 LinearModel and Rank Estimation 252 10.2.1 Penalty R-Estimators 256 10.2.2 PTREs and Stein-type R-Estimators 258 10.3 Asymptotic Distributional Bias and L2 Risk of the R-Estimators 259 10.3.1 HardThreshold Estimators (Subset Selection) 259 10.3.2 Rank-based LASSO 260 10.3.3 Multivariate Normal DecisionTheory and Oracles for Diagonal Linear Projection 261 10.4 Comparison of Estimators 262 10.4.1 Comparison of RE with Restricted RE 262 10.4.2 Comparison of RE with PTRE 263 10.4.3 Comparison of RE with SRE and PRSRE 263 10.4.4 Comparison of RE and Restricted RE with RRRE 265 10.4.5 Comparison of RRRE with PTRE, SRE, and PRSRE 266 10.4.6 Comparison of RLASSO with RE and Restricted RE 267 10.4.7 Comparison of RLASSO with PTRE, SRE, and PRSRE 267 10.4.8 Comparison of Modified RLASSO with RRRE 268 10.5 Summary and Concluding Remarks 268 11 High-Dimensional Ridge Regression 285 11.1 High-Dimensional RRE 286 11.2 High-Dimensional Stein-Type RRE 288 11.2.1 Numerical Results 291 11.2.1.1 Example: Riboflavin Data 291 11.2.1.2 Monte Carlo Simulation 291 11.3 Post Selection Shrinkage 293 11.3.1 Notation and Assumptions 296 11.3.2 Estimation Strategy 297 11.3.3 Asymptotic Distributional L2-Risks 299 11.4 Summary and Concluding Remarks 300 12 Applications: Neural Networks and Big Data 303 12.1 Introduction 304 12.2 A Simple Two-Layer Neural Network 307 12.2.1 Logistic Regression Revisited 307 12.2.2 Logistic Regression Loss Function with Penalty 310 12.2.3 Two-Layer Logistic Regression 311 12.3 Deep Neural Networks 313 12.4 Application: Image Recognition 315 12.4.1 Background 315 12.4.2 Binary Classification 316 12.4.3 Image Preparation 318 12.4.4 Experimental Results 320 12.5 Summary and Concluding Remarks 323 References 325 Index 333

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Book SynopsisFeaturing a multidisciplinary approach with practical examples from biology, gerontology, and demography, The Biostatistics of Aging provides a statistical theoretical framework for aging and aging-related diseases in addition to genetic and environmental contributions to mortality.Table of ContentsPREFACE AND ACKNOWLEDGMENT ix 1 Introduction 1 2 An Account of Gompertzian Mortality through Statistical and Evolutionary Arguments 6 2.1 The Statistical Theory of Extreme Values 10 2.2 The Evolutionary Theory of Aging 36 3 The Argument against Gompertzian Mortality 69 3.1 Departures from the Gompertz Model 70 3.2 An Evolution-Based Model of Causation 72 4 The Index of Aging-Relatedness 93 4.1 A Survival Mixture Model of the Gompertz and Weibull Distributions 94 4.2 Definition and Interpretation of the Index of Aging-Relatedness 97 4.3 The Survival Mixture Model and Competing Risks 103 4.4 Estimation of the Model Parameters 107 4.5 Illustrative Application: The Israeli Ischemic Heart Disease Study 109 4.6 Precision of Estimation 122 5 Discussion: Implications 128 5.1 The Meaning of the Gompertz Parameter 128 5.2 Age as a Risk Factor for Disease 132 5.3 Are Aging-Related Diseases an Integral Part of Aging? 134 5.4 Biological versus Chronological Aging 135 5.5 The Public Health Notion of Compression of Morbidity 138 5.6 A Picture of Aging for the Twenty-First Century 143 APPENDIX A: PROOFS OF RESULTS IN SECTION 2.1.2 WITH SOME EXTENSIONS 154 APPENDIX B: DERIVATION OF HAMILTON’S EQUATION FOR THE FORCE OF NATURAL SELECTION ON MORTALITY 170 APPENDIX C: SOME PROPERTIES OF THE GOMPERTZ AND WEIBULL DISTRIBUTIONS 174 APPENDIX D: FIRST AND SECOND PARTIAL DERIVATIVES OF THE MIXTURE LOG-LIKELIHOOD FUNCTION 178 APPENDIX E: EXPECTATION–CONDITIONAL MAXIMIZATION (ECM) ALGORITHM 183 APPENDIX F: R PROGRAM 190 REFERENCES 226 AUTHOR INDEX 245 SUBJECT INDEX 253

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Book SynopsisAircraft Flight Dynamics and Control addresses airplane flight dynamics and control in a largely classical manner, but with references to modern treatment throughout.Trade ReviewAlthough not a replacement for Bernard Etkins Dynamics of Atmospheric Flight or Mike Cook s Flight Dynamic Principles, it is an ideal companion book for students and those beginning their careers in flight dynamics and control. (The Aeronautical Journal, 1 June 2014) Written by an author with experience as an engineering test pilot as well as a university professor, Aircraft Flight Dynamics and Control provides the reader with a systematic development of the insights and tools necessary for further work in related fields of flight dynamics and control. It is an ideal course textbook and is also a valuable reference for many of the necessary basic formulations of the math and science underlying flight dynamics and control. (Expofairs.com, 15 May 2014)Table of ContentsSeries Preface xiii Glossary xv 1 Introduction 1 1.1 Background 1 1.2 Overview 2 1.3 Customs and Conventions 6 2 Coordinate Systems 7 2.1 Background 7 2.2 The Coordinate Systems 7 2.2.1 The inertial reference frame, FI 7 2.2.2 The earth-centered reference frame, FEC 8 2.2.3 The earth-fixed reference frame, FE 8 2.2.4 The local-horizontal reference frame, FH 8 2.2.5 Body-fixed reference frames, FB 10 2.2.6 Wind-axis system, FW 12 2.2.7 Atmospheric reference frame 12 2.3 Vector Notation 13 2.4 Customs and Conventions 14 2.4.1 Latitude and longitude 14 2.4.2 Body axes 14 2.4.3 'The' body-axis system 14 2.4.4 Aerodynamic angles 15 3 Coordinate System Transformations 17 3.1 Problem Statement 17 3.2 Transformations 18 3.2.1 Definitions 18 3.2.2 Direction cosines 18 3.2.3 Euler angles 21 3.2.4 Euler parameters 25 3.3 Transformations of Systems of Equations 26 3.4 Customs and Conventions 27 3.4.1 Names of Euler angles 27 3.4.2 Principal values of Euler angles 27 4 Rotating Coordinate Systems 31 4.1 General 31 4.2 Direction Cosines 34 4.3 Euler Angles 34 4.4 Euler Parameters 36 4.5 Customs and Conventions 38 4.5.1 Angular velocity components 38 5 Inertial Accelerations 43 5.1 General 43 5.2 Inertial Acceleration of a Point 43 5.2.1 Arbitrary moving reference frame 43 5.2.2 Earth-centered moving reference frame 46 5.2.3 Earth-fixed moving reference frame 46 5.3 Inertial Acceleration of a Mass 47 5.3.1 Linear acceleration 48 5.3.2 Rotational acceleration 49 5.4 States 53 5.5 Customs and Conventions 53 5.5.1 Linear velocity components 53 5.5.2 Angular velocity components 54 5.5.3 Forces 54 5.5.4 Moments 56 5.5.5 Groupings 56 6 Forces and Moments 59 6.1 General 59 6.1.1 Assumptions 59 6.1.2 State variables 60 6.1.3 State rates 60 6.1.4 Flight controls 60 6.1.5 Independent variables 62 6.2 Non-Dimensionalization 62 6.3 Non-Dimensional Coefficient Dependencies 63 6.3.1 General 63 6.3.2 Altitude dependencies 64 6.3.3 Velocity dependencies 64 6.3.4 Angle-of-attack dependencies 64 6.3.5 Sideslip dependencies 66 6.3.6 Angular velocity dependencies 68 6.3.7 Control dependencies 69 6.3.8 Summary of dependencies 70 6.4 The Linear Assumption 71 6.5 Tabular Data 71 6.6 Customs and Conventions 72 7 Equations of Motion 75 7.1 General 75 7.2 Body-Axis Equations 75 7.2.1 Body-axis force equations 75 7.2.2 Body-axis moment equations 76 7.2.3 Body-axis orientation equations (kinematic equations) 77 7.2.4 Body-axis navigation equations 77 7.3 Wind-Axis Equations 78 7.3.1 Wind-axis force equations 78 7.3.2 Wind-axis orientation equations (kinematic equations) 80 7.3.3 Wind-axis navigation equations 81 7.4 Steady-State Solutions 81 7.4.1 General 81 7.4.2 Special cases 83 7.4.3 The trim problem 88 8 Linearization 93 8.1 General 93 8.2 Taylor Series 94 8.3 Nonlinear Ordinary Differential Equations 95 8.4 Systems of Equations 95 8.5 Examples 97 8.5.1 General 97 8.5.2 A kinematic equation 99 8.5.3 A moment equation 100 8.5.4 A force equation 103 8.6 Customs and Conventions 105 8.6.1 Omission of Δ 105 8.6.2 Dimensional derivatives 105 8.6.3 Added mass 105 8.7 The Linear Equations 106 8.7.1 Linear equations 106 8.7.2 Matrix forms of the linear equations 108 9 Solutions to the Linear Equations 113 9.1 Scalar Equations 113 9.2 Matrix Equations 114 9.3 Initial Condition Response 115 9.3.1 Modal analysis 115 9.4 Mode Sensitivity and Approximations 120 9.4.1 Mode sensitivity 120 9.4.2 Approximations 123 9.5 Forced Response 124 9.5.1 Transfer functions 124 9.5.2 Steady-state response 125 10 Aircraft Flight Dynamics 127 10.1 Example: Longitudinal Dynamics 127 10.1.1 System matrices 127 10.1.2 State transition matrix and eigenvalues 127 10.1.3 Eigenvector analysis 129 10.1.4 Longitudinal mode sensitivity and approximations 132 10.1.5 Forced response 137 10.2 Example: Lateral–Directional Dynamics 140 10.2.1 System matrices 140 10.2.2 State transition matrix and eigenvalues 140 10.2.3 Eigenvector analysis 142 10.2.4 Lateral–directional mode sensitivity and approximations 144 10.2.5 Forced response 148 11 Flying Qualities 151 11.1 General 151 11.1.1 Method 152 11.1.2 Specifications and standards 155 11.2 MIL-F-8785C Requirements 156 11.2.1 General 156 11.2.2 Longitudinal flying qualities 157 11.2.3 Lateral–directional flying qualitities 158 12 Automatic Flight Control 169 12.1 Simple Feedback Systems 170 12.1.1 First-order systems 170 12.1.2 Second-order systems 172 12.1.3 A general representation 177 12.2 Example Feedback Control Applications 178 12.2.1 Roll mode 178 12.2.2 Short-period mode 184 12.2.3 Phugoid 188 12.2.4 Coupled roll–spiral oscillation 198 13 Trends in Automatic Flight Control 209 13.1 Overview 209 13.2 Dynamic Inversion 210 13.2.1 The controlled equations 212 13.2.2 The kinematic equations 215 13.2.3 The complementary equations 221 13.3 Control Allocation 224 13.3.1 Background 224 13.3.2 Problem statement 225 13.3.3 Optimality 231 13.3.4 Sub-optimal solutions 232 13.3.5 Optimal solutions 235 13.3.6 Near-optimal solutions 241 Problems 243 References 244 A Example Aircraft 247 Reference 253 B Linearization 255 B.1 Derivation of Frequently Used Derivatives 255 B.2 Non-dimensionalization of the Rolling Moment Equation 257 B.3 Body Axis Z-Force and Thrust Derivatives 258 B.4 Non-dimensionalization of the Z-Force Equation 260 C Derivation of Euler Parameters 263 D Fedeeva's Algorithm 269 Reference 272 E MATLAB Commands Used in the Text 273 E.1 Using MATLAB 273 E.2 Eigenvalues and Eigenvectors 274 E.3 State-Space Representation 274 E.4 Transfer Function Representation 275 E.5 Root Locus 277 E.6 MATLAB® Functions (m-files) 277 E.6.1 Example aircraft 278 E.6.2 Mode sensitivity matrix 278 E.6.3 Cut-and-try root locus gains 278 E.7 Miscellaneous Applications and Notes 280 E.7.1 Matrices 280 E.7.2 Commands used to create Figures 10.2 and 10.3 281 Index 283

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Book SynopsisSystem Simulation Techniques with MATLAB and Simulink comprehensively explains how to use MATLAB and Simulink to perform dynamic systems simulation tasks for engineering and non-engineering applications.Table of ContentsForeword xiiiPreface xv1 Introduction to System Simulation Techniques and Applications 11.1 Overview of System Simulation Techniques 11.2 Development of Simulation Software 21.3 Introduction to MATLAB 51.4 Structure of the Book 7Exercises 9References 92 Fundamentals of MATLAB Programming 112.1 MATLAB Environment 112.2 Data Types in MATLAB 132.3 Matrix Computations in MATLAB 162.5 Programming and Tactics of MATLAB Functions 232.6 Two-dimensional Graphics in MATLAB 272.7 Three-dimensional Graphics 332.8 Graphical User Interface Design in MATLAB 362.9 Accelerating MATLAB Functions 52Exercises 60References 633 MATLAB Applications in Scientific Computations 653.1 Analytical and Numerical Solutions 663.2 Solutions to Linear Algebra Problems 673.3 Solutions of Calculus Problems 853.4 Solutions of Ordinary Differential Equations 913.5 Nonlinear Equation Solutions and Optimization 1103.6 Dynamic Programming and its Applications in Path Planning 1203.7 Data Interpolation and Statistical Analysis 124Exercises 136References 1424 Mathematical Modeling and Simulation with Simulink 1454.1 Brief Description of the Simulink Block Library 1464.2 Simulink Modeling 1594.3 Model Manipulation and Simulation Analysis 1644.4 Illustrative Examples of Simulink Modeling 1724.5 Modeling, Simulation and Analysis of Linear Systems 1804.6 Simulation of Continuous Nonlinear Stochastic Systems 184Exercises 188References 1915 Commonly Used Blocks and Intermediate-level Modeling Skills 1935.1 Commonly Used Blocks and Modeling Skills 1935.2 Modeling and Simulation of Multivariable Linear Systems 2025.3 Nonlinear Components with Lookup Table Blocks 2095.4 Block Diagram Based Solutions of Differential Equations 2175.5 Output Block Library 2265.6 Three-dimensional Animation of Simulation Results 2385.7 Subsystems and Block Masking Techniques 245Exercises 260References 2646 Advanced Techniques in Simulink Modeling and Applications 2656.1 Command-line Modeling in Simulink 2656.2 System Simulation and Linearization 2726.3 S-function Programming and Applications 2806.4 Examples of Optimization in Simulation: Optimal Controller Design Applications 296Exercises 303References 3067 Modeling and Simulation of Engineering Systems 3077.1 Physical System Modeling with Simscape 3087.2 Description of SimPowerSystems 3187.3 Modeling and Simulation of Electronic Systems 3227.4 Simulation of Motors and Electric Drive Systems 3367.5 Modeling and Simulation of Mechanical Systems 346Exercises 360References 3628 Modeling and Simulation of Non-Engineering Systems 3638.1 Modeling and Simulation of Pharmacokinetics Systems 3638.2 Video and Image Processing Systems 3768.3 Finite State Machine Simulation and Stateflow Applications 3908.4 Simulation of Discrete Event Systems with SimEvents 408Exercises 416References 4179 Hardware-in-the-loop Simulation and Real-time Control 4199.1 Simulink and Real-Time Workshop 4199.2 Introduction to dSPACE and its Blocks 4299.3 Introduction to Quanser and its Blocks 4309.4 Hardware-in-the-loop Simulation and Real-time Control Examples 4339.5 Low Cost Solutions with NIAT 4399.6 HIL Solutions with Even Lower Costs 4469.6.3 The MESABox 449Exercises 450References 451Appendix: Functions and Models 453Index 459

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Book SynopsisWritten by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics.Table of ContentsPREFACE ix PART I THE BASICS OF ENUMERATIVE COMBINATORICS 1 Initial EnCOUNTers with Combinatorial Reasoning 3 1.1 Introduction 3 1.2 The Pigeonhole Principle 3 1.3 Tiling Chessboards with Dominoes 13 1.4 Figurate Numbers 18 1.5 Counting Tilings of Rectangles 24 1.6 Addition and Multiplication Principles 33 1.7 Summary and Additional Problems 46 References 50 2 Selections, Arrangements, and Distributions 51 2.1 Introduction 51 2.2 Permutations and Combinations 52 2.3 Combinatorial Models 64 2.4 Permutations and Combinations with Repetitions 77 2.5 Distributions to Distinct Recipients 86 2.6 Circular Permutations and Derangements 100 2.7 Summary and Additional Problems 109 Reference 112 3 Binomial Series and Generating Functions 113 3.1 Introduction 113 3.2 The Binomial and Multinomial Theorems 114 3.3 Newton’s Binomial Series 122 3.4 Ordinary Generating Functions 131 3.5 Exponential Generating Functions 147 3.6 Summary and Additional Problems 163 References 166 4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim 167 4.1 Introduction 167 4.2 Evaluating Alternating Sums with the DIE Method 168 4.3 The Principle of Inclusion–Exclusion (PIE) 179 4.4 Rook Polynomials 191 4.5 (Optional) Zeckendorf Representations and Fibonacci Nim 202 4.6 Summary and Additional Problems 207 References 210 5 Recurrence Relations 211 5.1 Introduction 211 5.2 The Fibonacci Recurrence Relation 212 5.3 Second-Order Recurrence Relations 222 5.4 Higher-Order Linear Homogeneous Recurrence Relations 233 5.5 Nonhomogeneous Recurrence Relations 247 5.6 Recurrence Relations and Generating Functions 257 5.7 Summary and Additional Problems 268 References 273 6 Special Numbers 275 6.1 Introduction 275 6.2 Stirling Numbers 275 6.3 Harmonic Numbers 296 6.4 Bernoulli Numbers 306 6.5 Eulerian Numbers 315 6.6 Partition Numbers 323 6.7 Catalan Numbers 335 6.8 Summary and Additional Problems 345 References 352 PART II TWO ADDITIONAL TOPICS IN ENUMERATION 7 Linear Spaces and Recurrence Sequences 355 7.1 Introduction 355 7.2 Vector Spaces of Sequences 356 7.3 Nonhomogeneous Recurrences and Systems of Recurrences 367 7.4 Identities for Recurrence Sequences 378 7.5 Summary and Additional Problems 390 8 Counting with Symmetries 393 8.1 Introduction 393 8.2 Algebraic Discoveries 394 8.3 Burnside’s Lemma 407 8.4 The Cycle Index and Pólya’s Method of Enumeration 417 8.5 Summary and Additional Problems 430 References 432 PART III NOTATIONS INDEX, APPENDICES, AND SOLUTIONS TO SELECTED ODD PROBLEMS Index of Notations 435 Appendix A Mathematical Induction 439 A.1 Principle of Mathematical Induction 439 A.2 Principle of Strong Induction 441 A.3 Well Ordering Principle 442 Appendix B Searching the Online Encyclopedia of Integer Sequences (OEIS) 443 B.1 Searching a Sequence 443 B.2 Searching an Array 444 B.3 Other Searches 444 B.4 Beginnings of OEIS 444 Appendix C Generalized Vandermonde Determinants 445 Hints, Short Answers, and Complete Solutions to Selected Odd Problems 449 INDEX 467

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Book SynopsisThis book provides a comprehensive introduction to multiple-point geostatistics, where spatial continuity is described using training images. Multiple-point geostatistics aims at bridging the gap between physical modelling/realism and spatio-temporal stochastic modelling. The book provides an overview of this new field in three parts. Part I presents a conceptual comparison between traditional random function theory and stochastic modelling based on training images, where random function theory is not always used. Part II covers in detail various algorithms and methodologies starting from basic building blocks in statistical science and computer science. Concepts such as non-stationary and multi-variate modeling, consistency between data and model, the construction of training images and inverse modelling are treated. Part III covers three example application areas, namely, reservoir modelling, mineral resources modelling and climate model downscaling. This book will be an invaluable rTrade Review"I benefited from this book and plan to keep it as a resource on my bookshelf. I recommend Multiple-point Geostatistics: Stochastic Modeling with Training Images to my peers in mathematical geosciences." (Mathematical Geosciences, 2016)Table of ContentsPreface, vii Acknowledgments, xi Part I Concepts I.1 Hiking in the Sierra Nevada, 3 I.2 Spatial estimation based on random function theory, 7 I.3 Universal kriging with training images, 29 I.4 Stochastic simulations based on random function theory, 49 I.5 Stochastic simulation without random function theory, 59 I.6 Returning to the Sierra Nevada, 75 Part II Methods II.1 Introduction, 87 II.2 The algorithmic building blocks, 91 II.3 Multiple-point geostatistics algorithms, 155 II.4 Markov random fields, 173 II.5 Nonstationary modeling with training images, 183 II.6 Multivariate modeling with training images, 199 II.7 Training image construction, 221 II.8 Validation and quality control, 239 II.9 Inverse modeling with training images, 259 II.10 Parallelization, 295 Part III Applications III.1 Reservoir forecasting – the West Coast of Africa (WCA) reservoir, 303 III.2 Geological resources modeling in mining, 329 Coauthored by Cristian P´erez, Julian M. Ortiz, & Alexandre Boucher III.3 Climate modeling application – the case of the Murray–Darling Basin, 345 Index, 361

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Book SynopsisA preeminent expert in the field explores new and exciting methodologies in the ever-growing field of robust statistics Used to develop data analytical methods, which are resistant to outlying observations in the data, while capable of detecting outliers, robust statistics is extremely useful for solving an array of common problems, such as estimating location, scale, and regression parameters. Written by an internationally recognized expert in the field of robust statistics, this book addresses a range of well-established techniques while exploring, in depth, new and exciting methodologies. Local robustness and global robustness are discussed, and problems of non-identifiability and adaptive estimation are considered. Rather than attempt an exhaustive investigation of robustness, the author provides readers with a timely review of many of the most important problems in statistical inference involving robust estimation, along with a brief look at confidence intervals for location. ThroTable of ContentsForeword xi Preface xv Acknowledgments xvii Notation xix Acronyms xxi About the Companion Website xxiii 1 Introduction to Asymptotic Convergence 1 1.1 Introduction, 1 1.2 Probability Spaces and Distribution Functions, 2 1.3 Laws of Large Numbers, 3 1.3.1 Convergence in Probability and Almost Sure, 3 1.3.2 Expectation and Variance, 4 1.3.3 Statements of the Law of Large Numbers, 4 1.3.4 Some History and an Example, 5 1.3.5 Some More Asymptotic Theory and Application, 6 1.4 The Modus Operandi Related by Location Estimation, 8 1.5 Efficiency of Location Estimators, 17 1.6 Estimation of Location and Scale, 20 2 The Functional Approach 27 2.1 Estimation and Conditions A, 27 2.2 Consistency, 37 2.3 Weak Continuity and Weak Convergence, 41 2.4 Fréchet Differentiability, 44 2.5 The Influence Function, 48 2.6 Efficiency for Multivariate Parameters, 51 2.7 Other Approaches, 52 3 More Results on Differentiability 59 3.1 Further Results on Fréchet Differentiability, 59 3.2 M-Estimators: Their Introduction, 59 3.2.1 Non-Smooth Analysis and Conditions A′, 61 3.2.2 Existence and Uniqueness for Solutions of Equations, 65 3.2.3 Results for M-estimators with Non-Smooth Ψ, 67 3.3 Regression M-Estimators, 70 3.4 Stochastic Fréchet Expansions and Further Considerations, 73 3.5 Locally Uniform Fréchet Expansion, 74 3.6 Concluding Remarks, 76 4 Multiple Roots 79 4.1 Introduction to Multiple Roots, 79 4.2 Asymptotics for Multiple Roots, 80 4.3 Consistency in the Face of Multiple Roots, 82 4.3.1 Preliminaries, 83 4.3.2 Asymptotic Properties of Roots and Tests, 92 4.3.3 Application of Asymptotic Theory, 94 4.3.4 Normal Mixtures and Conclusion, 97 5 Differentiability and Bias Reduction 99 5.1 Differentiability, Bias Reduction, and Variance Estimation, 99 5.1.1 The Jackknife Bias and Variance Estimation, 99 5.1.2 Simple Location and Scale Bias Adjustments, 102 5.1.3 The Bootstrap, 105 5.1.4 The Choice to Jackknife or Bootstrap, 107 5.2 Further Results on the Newton Algorithm, 108 6 Minimum Distance Estimation and Mixture Estimation 113 6.1 Minimum Distance Estimation and Revisiting Mixture Modeling, 113 6.2 The L2-Minimum Distance Estimator for Mixtures, 125 6.2.1 The L2-Estimator for Mixing Proportions, 126 6.2.2 The L2-Estimator for Switching Regressions, 130 6.2.3 An Example Application of Switching Regressions, 133 6.3 Other Minimum Distance Estimation Applications, 135 6.3.1 Mixtures of Exponential Distributions, 136 6.3.2 Gamma Distributions and Quality Assurance, 139 7 L-Estimates and Trimmed Likelihood Estimates 147 7.1 A Preview of Estimation Using Order Statistics, 147 7.1.1 The Functional Form of L-Estimators of Location, 150 7.2 The Trimmed Likelihood Estimator, 152 7.2.1 LTS and Breakdown Point, 154 7.2.2 TLE Asymptotics for the Normal Distribution, 156 7.3 Adaptive Trimmed Likelihood and Identification of Outliers, 160 7.4 Adaptive Trimmed Likelihood in Regression, 163 7.5 What to do if n is Large?, 169 7.5.1 TLE Asymptotics for Location and Regression, 170 8 Trimmed Likelihood for Multivariate Data 175 8.1 Identification of Multivariate Outliers, 175 9 Further Directions and Conclusion 181 9.1 A Way Forward, 181 Appendix A Specific Proof of Theorem 2.1 187 Appendix B Specific Calculations in Examples 4.1 and 4.2 189 Appendix C Calculation of Moments in Example 4.2 193 Bibliography 195 Index 211

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Book SynopsisFeatures the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical GeomeTrade Review“The book is an extremely valuable compendium of elementary constructions of Euclidean geometry. The text, especially the proofs, is clearly structured and move forward in simple steps, and thus are at the one hand very suitable for a beginner in geometry and at the other hand exemplary for a teacher of geometry.” (Zentralblatt MATH, 1 October 2014) Table of ContentsPreface v PART I EUCLIDEAN GEOMETRY 1 Congruency 3 1.1 Introduction 3 1.2 Congruent Figures 6 1.3 Parallel Lines 12 1.3.1 Angles in a Triangle 13 1.3.2 Thales' Theorem 14 1.3.3 Quadrilaterals 17 1.4 More About Congruency 21 1.5 Perpendiculars and Angle Bisectors 24 1.6 Construction Problems 28 1.6.1 The Method of Loci 31 1.7 Solutions to Selected Exercises 33 1.8 Problems 38 2 Concurrency 41 2.1 Perpendicular Bisectors 41 2.2 Angle Bisectors 43 2.3 Altitudes 46 2.4 Medians 48 2.5 Construction Problems 50 2.6 Solutions to the Exercises 54 2.7 Problems 56 3 Similarity 59 3.1 Similar Triangles 59 3.2 Parallel Lines and Similarity 60 3.3 Other Conditions Implying Similarity 64 3.4 Examples 67 3.5 Construction Problems 75 3.6 The Power of a Point 82 3.7 Solutions to the Exercises 87 3.8 Problems 90 4 Theorems of Ceva and Menelaus 95 4.1 Directed Distances, Directed Ratios 95 4.2 The Theorems 97 4.3 Applications of Ceva's Theorem 99 4.4 Applications of Menelaus' Theorem 103 4.5 Proofs of the Theorems 115 4.6 Extended Versions of the Theorems 125 4.6.1 Ceva's Theorem in the Extended Plane 127 4.6.2 Menelaus' Theorem in the Extended Plane 129 4.7 Problems 131 5 Area 133 5.1 Basic Properties 133 5.1.1 Areas of Polygons 134 5.1.2 Finding the Area of Polygons 138 5.1.3 Areas of Other Shapes 139 5.2 Applications of the Basic Properties 140 5.3 Other Formulae for the Area of a Triangle 147 5.4 Solutions to the Exercises 153 5.5 Problems 153 6 Miscellaneous Topics 159 6.1 The Three Problems of Antiquity 159 6.2 Constructing Segments of Specific Lengths 161 6.3 Construction of Regular Polygons 166 6.3.1 Construction of the Regular Pentagon 168 6.3.2 Construction of Other Regular Polygons 169 6.4 Miquel's Theorem 171 6.5 Morley's Theorem 178 6.6 The Nine-Point Circle 185 6.6.1 Special Cases 188 6.7 The Steiner-Lehmus Theorem 193 6.8 The Circle of Apollonius 197 6.9 Solutions to the Exercises 200 6.10 Problems 201 PART II TRANSFORMATIONAL GEOMETRY 7 The Euclidean Transformations or Isometries 207 7.1 Rotations, Reflections, and Translations 207 7.2 Mappings and Transformations 211 7.2.1 Isometries 213 7.3 Using Rotations, Reflections, and Translations 217 7.4 Problems 227 8 The Algebra of Isometries 231 8.1 Basic Algebraic Properties 231 8.2 Groups of Isometries 236 8.2.1 Direct and Opposite Isometries 237 8.3 The Product of Reflections 241 8.4 Problems 246 9 The Product of Direct Isometries 253 9.1 Angles 253 9.2 Fixed Points 255 9.3 The Product of Two Translations 256 9.4 The Product of a Translation and a Rotation 257 9.5 The Product of Two Rotations 260 9.6 Problems 263 10 Symmetry and Groups 269 10.1 More About Groups 269 10.1.1 Cyclic and Dihedral Groups 273 10.2 Leonardo's Theorem 277 10.3 Problems 281 11 Homotheties 287 11.1 The Pantograph 287 11.2 Some Basic Properties 288 11.2.1 Circles 291 11.3 Construction Problems 293 11.4 Using Homotheties in Proofs 298 11.5 Dilatation 302 11.6 Problems 304 12 Tessellations 311 12.1 Tilings 311 12.2 Monohedral Tilings 312 12.3 Tiling with Regular Polygons 317 12.4 Platonic and Archimedean Tilings 323 12.5 Problems 330 PART III INVERSIVE AND PROJECTIVE GEOMETRIES 13 Introduction to Inversive Geometry 337 13.1 Inversion in the Euclidean Plane 337 13.2 The Effect of Inversion on Euclidean Properties 343 13.3 Orthogonal Circles 351 13.4 Compass-Only Constructions 360 13.5 Problems 369 14 Reciprocation and the Extended Plane 373 14.1 Harmonic Conjugates 373 14.2 The Projective Plane and Reciprocation 383 14.3 Conjugate Points and Lines 393 14.4 Conics 399 14.5 Problems 406 15 Cross Ratios 409 15.1 Cross Ratios 409 15.2 Applications of Cross Ratios 420 15.3 Problems 429 16 Introduction to Projective Geometry 433 16.1 Straightedge Constructions 433 16.2 Perspectivities and Projectivities 443 16.3 Line Perspectivities and Line Projectivities 448 16.4 Projective Geometry and Fixed Points 448 16.5 Projecting a Line to Infinity 451 16.6 The Apollonian Definition of a Conic 455 16.7 Problems 461 Bibliography 464 Index 469

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Book SynopsisTable of ContentsPreface xix About the Companion Website xxiii Part I Philosophy and Fundamentals 1 1 Introduction to Quality Control and the Total Quality System 3 1-1 Introduction and Chapter Objectives 3 1-2 Evolution of Quality Control 4 1-3 Quality 7 1-4 Quality Control 12 1-5 Quality Assurance 13 1-6 Quality Circles and Quality Improvement Teams 14 1-7 Customer Needs and Market Share 15 1-8 Benefits of Quality Control and the Total Quality System 16 1-9 Quality and Reliability 18 1-10 Quality Improvement 18 1-11 Product and Service Costing 19 1-12 Quality Costs 23 1-13 Measuring Quality Costs 27 1-14 Management of Quality 31 1-15 Quality and Productivity 34 1-16 Total Quality Environmental Management 37 Summary 40 Key Terms 41 Exercises 41 References 46 2 Some Philosophies and Their Impact on Quality 47 2-1 Introduction and Chapter Objectives 47 2-2 Service Industries and Their Characteristics 47 2-3 Model for Service Quality 53 2-4 W. Edwards Deming’s Philosophy 56 2-5 Philip B. Crosby’s Philosophy 75 2-6 Joseph M. Juran’s Philosophy 78 2-7 The Three Philosophies Compared 82 Summary 85 Key Terms 85 Exercises 86 References 88 3 Quality Management: Practices, Tools, and Standards 89 3-1 Introduction and Chapter Objectives 89 3-2 Management Practices 90 3-3 Quality Function Deployment 99 3-4 Benchmarking and Performance Evaluation 106 3-5 Health Care Analytics 115 3-6 Tools for Continuous Quality Improvement 124 3-7 International Standards ISO 9000 and Other Derivatives 137 Part II Statistical Foundations and Methods of Quality Improvement 147 4 Fundamentals of Statistical Concepts and Techniques in Quality Control and Improvement 149 4-1 Introduction and Chapter Objectives 150 4-2 Population and Sample 150 4-3 Parameter and Statistic 150 4-4 Probability 151 4-5 Descriptive Statistics: Describing Product or Process Characteristics 156 4-6 Probability Distributions 173 4-7 Inferential Statistics: Drawing Conclusions on Product and Process Quality 189 Summary 212 Appendix: Approximations to Some Probability Distributions 212 Key Terms 215 Exercises 216 References 228 5 Data Analyses and Sampling 229 5-1 Introduction and Chapter Objectives 229 5-2 Empirical Distribution Plots 230 5-3 Randomness of a Sequence 235 5-4 Validating Distributional Assumptions 237 5-5 Transformations to Achieve Normality 240 5-6 Analysis of Count Data 244 5-7 Analysis of Customer Satisfaction Data 248 5-8 Concepts in Sampling 257 Summary 264 Key Terms 265 Exercises 266 References 272 Part III Statistical Process Control 273 6 Statistical Process Control Using Control Charts 275 6-1 Introduction and Chapter Objectives 275 6-2 Causes of Variation 277 6-3 Statistical Basis for Control Charts 277 6-4 Selection of Rational Samples 289 6-5 Analysis of Patterns in Control Charts 290 6-6 Maintenance of Control Charts 294 Summary 295 Key Terms 295 Exercises 295 References 298 7 Control Charts for Variables 299 7-1 Introduction and Chapter Objectives 300 7-2 Selection of Characteristics for Investigation 301 7-3 Preliminary Decisions 302 7-4 Control Charts for the Mean and Range 303 7-5 Control Charts for the Mean and Standard Deviation 321 7-6 Control Charts for Individual Units 326 7-7 Control Charts for Short Production Runs 330 7-8 Other Control Charts 332 7-9 Risk-Adjusted Control Charts 352 7-10 Multivariate Control Charts 359 Summary 372 Key Terms 373 Exercises 374 References 387 8 Control Charts for Attributes 389 8-1 Introduction and Chapter Objectives 390 8-2 Advantages and Disadvantages of Attribute Charts 390 8-3 Preliminary Decisions 392 8-4 Chart for Proportion Nonconforming: p-Chart 392 8-5 Chart for Number of Nonconforming Items: np-Chart 409 8-6 Chart for Number of Nonconformities: c-Chart 411 8-7 Chart for Number of Nonconformities Per Unit: u-Chart 417 8-8 Chart for Demerits Per Unit: u-Chart 423 8-9 Charts for Highly Conforming Processes 426 8-10 Operating Characteristic Curves for Attribute Control Charts 431 Summary 434 Key Terms 435 Exercises 435 References 448 9 Process Capability Analysis 449 9-1 Introduction and Chapter Objectives 449 9-2 Specification Limits and Control Limits 450 9-3 Process Capability Analysis 451 9-4 Natural Tolerance Limits 453 9-5 Specifications and Process Capability 454 9-6 Process Capability Indices 457 9-7 Process Capability Analysis Procedures 476 9-8 Capability Analysis for Nonnormal Distributions 478 9-9 Setting Tolerances on Assemblies and Components 480 9-10 Estimating Statistical Tolerance Limits of a Process 487 Summary 489 Key Terms 490 Exercises 490 References 499 Part IV Acceptance Sampling 501 10 Acceptance Sampling Plans for Attributes and Variables 503 10-1 Introduction and Chapter Objectives 504 10-2 Advantages and Disadvantages of Sampling 504 10-3 Producer and Consumer Risks 505 10-4 Operating Characteristic Curve 505 10-5 Types of Sampling Plans 509 10-6 Evaluating Sampling Plans 511 10-7 Bayes Rule and Decision Making Based on Samples 516 10-8 Lot-by-Lot Attribute Sampling Plans 519 10-9 Other Attribute Sampling Plans 537 10-10 Deming’s kp Rule 540 10-11 Sampling Plans for Variables 543 10-12 Variable Sampling Plans for a Process Parameter 544 10-13 Variable Sampling Plans for Estimating the Lot Proportion Nonconforming 550 Summary 555 Key Terms 556 Exercises 556 References 562 Part V Product and Process Design 563 11 Reliability 565 11-1 Introduction and Chapter Objectives 565 11-2 Reliability 566 11-3 Life-Cycle Curve and Probability Distributions in Modeling Reliability 566 11-4 System Reliability 570 11-5 Operating Characteristic Curves 578 11-6 Reliability and Life Testing Plans 580 11-7 Survival Analysis 588 Summary 599 Key Terms 599 Exercises 600 References 603 12 Experimental Design and the Taguchi Method 605 12-1 Introduction and Chapter Objectives 606 12-2 Experimental Design Fundamentals 606 12-3 Some Experimental Designs 611 12-4 Factorial Experiments 631 12-5 The Taguchi Method 659 12-6 The Taguchi Philosophy 660 12-7 Loss Functions 663 12-8 Signal-to-Noise Ratio and Performance Measures 670 12-9 Critique of S/N Ratios 673 12-10 Experimental Design in the Taguchi Method 674 12-11 Parameter Design in the Taguchi Method 690 12-12 Critique of Experimental Design and the Taguchi Method 694 Summary 696 Key Terms 697 Exercises 698 References 708 13 Process Modeling Through Regression Analysis 711 13-1 Introduction and Chapter Objectives 711 13-2 Deterministic and Probabilistic Models 712 13-3 Model Assumptions 714 13-4 Least Squares Method for Parameter Estimation 716 13-5 Model Validation and Remedial Measures 722 13-6 Estimation and Inferences from a Regression Model 726 13-7 Qualitative Independent Variables 732 13-9 Logistic Regression 742 Summary 746 Key Terms 747 Exercises 748 References 752 Appendixes 753 A-1 Cumulative Binomial Distribution 753 A-2 Cumulative Poisson Distribution 758 A-3 Cumulative Standard Normal Distribution 760 A-4 Values of t for a Specified Right-Tail Area 763 A-5 Chi-Squared Values for a Specified Right-Tail Area 765 A-6 Values of F for a Specified Right-Tail Area 767 A-7 Factors for Computing Centerline and Three-Sigma Control Limits 773 A-8 Uniform Random Numbers 774 Index 775

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Book SynopsisFeatures a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author's primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equaTable of ContentsPreface ix 1. Introduction to Partial Differentiation Equation Analysis: Chemotaxis 1 2. Pattern Formation 43 3. Belousov–Zhabotinskii Reaction System 103 4. Hodgkin–Huxley and Fitzhugh–Nagumo Models 127 5. Anesthesia Spatiotemporal Distribution 163 6. Influenza with Vaccination and Diffusion 207 7. Drug Release Tracking 243 8. Temperature Distributions in Cryosurgery 287 Index 323

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Book SynopsisA comprehensive and accessible guide to panel data analysis using EViews software This book explores the use of EViews software in creating panel data analysis using appropriate empirical models and real datasets.Table of ContentsPreface xv About the Author xxi PART ONE PANEL DATA AS A MULTIVARIATE TIME SERIES BY STATES 1 1 Data Analysis Based on a Single Time Series by States 3 1.1 Introduction 3 1.2 Multivariate Growth Models 3 1.3 Alternative Multivariate Growth Models 10 1.4 Various Models Based on Correlated States 14 1.5 Seemingly Causal Models with Time-Related Effects 21 1.6 The Application of the Object POOL 23 1.7 Growth Models of Sample Statistics 29 1.8 Special Notes on Time-State Observations 32 1.9 Growth Models with an Environmental Variable 32 1.10 Models with an Environmental Multivariate 40 1.11 Special Piece-Wise Models 49 2 Data Analysis Based on Bivariate Time Series by States 55 2.1 Introduction 55 2.2 Models Based on Independent States 56 2.3 Time-Series Models Based on Two Correlated States 60 2.4 Time-Series Models Based on Multiple Correlated States 72 2.5 Time-Series Models with an Environmental Variable Zt, Based on Independent States 78 2.6 Models Based on Correlated States 82 2.7 Piece-Wise Time-Series Models 86 3 Data Analysis Based on Multivariate Time Series by States 87 3.1 Introduction 87 3.2 Models Based on (X_i,Y_i,Z_i) for Independent States 88 3.3 Models Based on (X_i, Y_i,Z_i) for Correlated States 90 3.4 Simultaneous SCMs with Trend 96 3.5 Models Based on (X1_i,X2_i,X3_i, Y1_i,Y2_i) for Independent States 100 3.6 Models Based on (X_i,Y_i) for Correlated States 103 3.7 Discontinuous Time-Series Models 106 3.8 Additional Examples for Correlated States 107 3.9 Special Notes and Comments 109 4 Applications of Seemingly Causal Models 111 4.1 Introduction 111 4.2 SCMs Based on a Single Time Series Y_it 112 4.3 SCMs Based on Bivariate Time Series (X_it,Y_it) 118 4.4 SCMs Based on a Trivariate (X1_i,X2_i,Y1_i) 120 4.5 SCMs Based on a Trivariate (X_it,Y1_it,Y2_it) 126 4.6 SCMs Based on Multivariate Endogenous and Exogenous Variables 127 4.7 Fixed- and Random Effects Models 133 4.8 Models with Cross-Section Specific Coefficients 138 4.9 Cases in Industry 146 PART TWO POOL PANEL DATA ANALYSIS 149 5 Evaluation Analysis 151 5.1 Introduction 151 5.2 Preliminary Evaluation Analysis 152 5.3 The Application of the Object “Descriptive Statistics and Tests” 153 5.4 Analysis Based on Ordinal Problem Indicators 158 5.5 Multiple Association between Categorical Variables 161 6 General Choice Models 165 6.1 Introduction 165 6.2 Multi-Factorial Binary Choice Models 165 6.3 Binary Logit Model of Yit on a Numerical Variable Xit 175 6.4 Binary Logit Model of a Zero-One Indicator Yit on (X1it,X2it) 182 6.5 Binary Choice Model of a Zero-One Indicator Yit on (X1it,X2it,X3it) 187 6.6 Binary Choice Model of a Zero-One Indicator Yit on (X1it,. . ., Xhit,. . .) 190 6.7 Special Notes and Comments 190 7 Advanced General Choice Models 192 7.1 Introduction 192 7.2 Categorical Data Analyses 193 7.3 Multi-Factorial Choice Models with a Numerical Independent Variable 207 8 Univariate General Linear Models 216 8.1 Introduction 216 8.2 ANOVA and Quantile Models 216 8.3 Continuous Linear-Effect Models 221 8.4 Piece-Wise Autoregressive Linear Models by Time Points 227 8.5 ANCOVA Models 241 9 Fixed-Effects Models and Alternatives 244 9.1 Introduction 244 9.2 Cross-Section Fixed-Effects Models 245 9.3 Time-Fixed-Effects Models 251 9.4 Two-Way Fixed-Effects Models 254 9.5 Extended Fixed-Effects Models 265 9.6 Selected Fixed-Effects Models from the Journal of Finance, 2011 274 9.7 Heterogeneous Regression Models 278 10 Special Notes on Selected Problems 286 10.1 Introduction 286 10.2 Problems with Dummy Variables 286 10.3 Problems with the Numerical Variable Rit 288 10.4 Problems with the First Difference Variable 294 10.5 Problems with Ratio Variables 295 10.6 The CAPM and its Extensions or Modifications 298 10.7 Selected Heterogeneous Regressions from International Journals 305 10.8 Models without the Time-Independent Variable 308 10.9 Models with Time Dummy Variables 311 10.10 Final Remarks 312 11 Seemingly Causal Models 314 11.1 Introduction 314 11.2 MANOVA Models 314 11.3 Multivariate Heterogeneous Regressions by Group and Time 315 11.4 MANCOVA Models 318 11.5 Discontinuous and Continuous MGLM by Time 319 11.6 Illustrative Linear-Effect Models by Times 319 11.7 Illustrative SCMs by Group and Time 331 PART THREE BALANCED PANEL DATA AS NATURAL EXPERIMENTAL DATA 337 12 Univariate Lagged Variables Autoregressive Models 339 12.1 Introduction 339 12.2 Developing Special Balanced Pool Data 339 12.3 Natural Experimental Data Analysis 341 12.4 The Simplest Heterogeneous Regressions 343 12.5 LVAR(1,1) Heterogeneous Regressions 344 12.6 Manual Stepwise Selection for General Linear LV(1) Model 362 12.7 Manual Stepwise Selection for Binary Choice LV(1) Models 369 12.8 Manual Stepwise Selection for Ordered Choice Models 378 12.9 Bounded Models by Group and Time 387 13 Multivariate Lagged Variables Autoregressive Models 396 13.1 Introduction 396 13.2 Seemingly Causal Models 396 13.3 Alternative Data Analyses 400 13.4 SCMs Based on (Y1,Y2) 401 13.5 Advanced Autoregressive SCMs 421 13.6 SCMs Based on (Y1,Y2) with Exogenous Variables 430 14 Applications of GLS Regressions 441 14.1 Introduction 441 14.2 Cross-Section Random Effects Models (CSREMs) 441 14.3 LV(1) CSREMs by Group or Time 443 14.4 CSREMs with the Numerical Time Variable 448 14.5 CSREMs by Time or Time Period 454 14.6 Period Random Effects Models (PEREMs) 463 14.7 Illustrative Panel Data Analysis Based on CES.wf1 465 14.8 Two-Way Effects Models 468 14.9 Testing Hypotheses 473 14.10 Generalized Method of Moments/Dynamic Panel Data 482 14.11 More Advanced Interaction Effects Models 489 References 501 Index 509

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Book SynopsisComplex networks such as the Internet, WWW, transportation networks, power grids, biological neural networks, and scientific cooperation networks of all kinds provide challenges for future technological development. The first systematic presentation of dynamical evolving networks, with many up-to-date applications and homework projects to enhance study The authors are all very active and well-known in the rapidly evolving field of complex networks Complex networks are becoming an increasingly important area of research Presented in a logical, constructive style, from basic through to complex, examining algorithms, through to construct networks and research challenges of the futureTable of ContentsAbout the Authors xi Preface xiii Acknowledgements xv Part I FUNDAMENTAL THEORY 1 Introduction 3 1.1 Background and Motivation 3 1.2 A Brief History of Complex Network Research 5 1.2.1 The Königsburg Seven-Bridge Problem 5 1.2.2 Random Graph Theory 7 1.2.3 Small-World Experiments 7 1.2.4 Strengths of Weak Ties 10 1.2.5 Heterogeneity and the WWW 10 1.3 New Era of Complex-Network Studies 11 Exercises 13 References 13 2 Preliminaries 15 2.1 Elementary Graph Theory 15 2.1.1 Background 15 2.1.2 Basic Concepts 15 2.1.3 Adjacency, Incidence and Laplacian Matrices 24 2.1.4 Degree Correlation and Assortativity 26 2.1.5 Some Basic Results on Graphs 31 2.1.6 Eulerian and Hamiltonian Graphs 35 2.1.7 Plane and Planar Graphs 37 2.1.8 Trees and Bipartite Graphs 39 2.1.9 Directed Graphs 41 2.1.10 Weighted Graphs 45 2.1.11 Some Applications 46 2.2 Elementary Probability and Statistics 52 2.2.1 Probability Preliminaries 52 2.2.2 Statistics Preliminaries 58 2.2.3 Law of Large Numbers and Central Limit Theorem 59 2.2.4 Markov Chains 61 2.3 Elementary Dynamical Systems Theory 62 2.3.1 Background and Motivation 62 2.3.2 Some Analytical Tools 70 2.3.3 Chaos in Nonlinear Systems 72 2.3.4 Kolmogorov-Sinai Entropy 77 2.3.5 Some Examples of Chaotic Systems 78 2.3.6 Stabilities of Nonlinear Systems 85 Exercises 90 References 100 3 Network Topologies: Basic Models and Properties 103 3.1 Introduction 103 3.2 Regular Networks 103 3.3 ER Random-Graph Model 105 3.4 Small-World Network Models 108 3.4.1 WS Small-World Network Model 108 3.4.2 NW Small-World Network Model 108 3.4.3 Statistical Properties of Small-World Network Models 109 3.5 Navigable Small-World Network Model 112 3.6 Scale-Free Network Models 114 3.6.1 BA Scale-Free Network Model 114 3.6.2 Robustness versus Fragility 118 3.6.3 Modified BA Models 122 3.6.4 A Simple Model with Power-Law Degree Distribution 126 3.6.5 Local-World and Multi-Local-World Network Models 126 Exercises 133 References 135 Part II APPLICATIONS - SELECTED TOPICS 4 Internet: Topology and Modeling 139 4.1 Introduction 139 4.2 Topological Properties of the Internet 141 4.2.1 Power–Law Node-Degree Distribution 141 4.2.2 Hierarchical Structure 143 4.2.3 Rich-Club Structure 145 4.2.4 Disassortative Property 147 4.2.5 Coreness and Betweenness 148 4.2.6 Growth of the Internet 151 4.2.7 Router-Level Internet Topology 152 4.2.8 Geographic Layout of the Internet 153 4.3 Random-Graph Network Topology Generator 155 4.4 Structural Network Topology Generators 156 4.4.1 Tiers Topology Generator 157 4.4.2 Transit–Stub Topology Generator 158 4.5 Connectivity-Based Network Topology Generators 159 4.5.1 Inet 160 4.5.2 BRITE Model 161 4.5.3 GLP Model 163 4.5.4 PFP Model 165 4.5.5 TANG Model 166 4.6 Multi-Local-World Model 167 4.6.1 Theoretical Considerations 167 4.6.2 Numerical Results with Comparison 169 4.6.3 Performance Comparison 176 4.7 HOT Model 178 4.8 Dynamical Behaviors of the Internet Topological Characteristics 181 4.9 Traffic Fluctuation on Weighted Networks 181 4.9.1 Weighted Networks 183 4.9.2 GRD Model 183 4.9.3 Data Traffic Fluctuations 184 References 190 5 Epidemic Spreading Dynamics 195 5.1 Introduction 195 5.2 Epidemic Threshold Theory 196 5.2.1 Epidemic (SI, SIS, SIR) Models 196 5.2.2 Epidemic Thresholds on Homogenous Networks 197 5.2.3 Statistical Data Analysis 198 5.2.4 Epidemic Thresholds on Heterogeneous Networks 199 5.2.5 Epidemic Thresholds on BA Networks 200 5.2.6 Epidemic Thresholds on Finite-Sized Scale-Free Networks 202 5.2.7 Epidemic Thresholds on Correlated Networks 202 5.2.8 SIR Model of Epidemic Spreading 203 5.2.9 Epidemic Spreading on Quenched Networks 205 5.3 Epidemic Spreading on Spatial Networks 206 5.3.1 Spatial Networks 206 5.3.2 Spatial Network Models for Infectious Diseases 207 5.3.3 Impact of Spatial Clustering on Disease Transmissions 209 5.3.4 Large-Scale Spatial Epidemic Spreading 211 5.3.5 Impact of Human Location-Specific Contact Patterns 212 5.4 Immunization on Complex Networks 213 5.4.1 Random Immunization 213 5.4.2 Targeted Immunization 213 5.4.3 Acquaintance Immunization 215 5.5 Computer Virus Spreading over the Internet 215 5.5.1 Random Constant-Spread Model 216 5.5.2 A Compartment-Based Model 217 5.5.3 Spreading Models of Email Viruses 219 5.5.4 Effects of Computer Virus on Network Topologies 221 References 222 6 Community Structures 225 6.1 Introduction 225 6.1.1 Various Scenarios in Real-World Social Networks 225 6.1.2 Generalization of Assortativity 226 6.2 Community Structure and Modularity 230 6.2.1 Community Structure 230 6.2.2 Modularity 230 6.2.3 Modularity of Weighted and Directed Networks 233 6.3 Modularity-Based Community Detecting Algorithms 234 6.3.1 CNM Scheme 234 6.3.2 BGLL Scheme 236 6.3.3 Multi-Slice Community Detection 237 6.3.4 Detecting Spatial Community Structures 240 6.4 Other Community Partitioning Schemes 240 6.4.1 Limitations of the Modularity Measure 240 6.4.2 Clique Percolation Scheme 242 6.4.3 Edge-Based Community Detection Scheme 244 6.4.4 Evaluation Criteria for Community Detection Algorithms 249 6.5 Some Recent Progress 253 References 253 7 Network Games 257 7.1 Introduction 257 7.2 Two-Player/Two-Strategy Evolutionary Games on Networks 261 7.2.1 Introduction to Games on Networks 261 7.2.2 Two-Player/Two-Strategy Games on Regular Lattices 261 7.2.3 Two-Player/Two-Strategy Games on BA Scale-Free Networks 264 7.2.4 Two-Player/Two-Strategy Games on Correlated Scale-Free Networks 267 7.2.5 Two-Player/Two-Strategy Games on Clustered Scale-Free Networks 271 7.3 Multi-Player/Two-Strategy Evolutionary Games on Networks 273 7.3.1 Introduction to Public Goods Game 273 7.3.2 Multi-Player/Two-Strategy Evolutionary Games on BA Networks 273 7.3.3 Multi-Player/Two-Strategy Evolutionary Games on Correlated Scale-free Networks 276 7.3.4 Multi-Player/Two-Strategy Evolutionary Games on Clustered Scale-free Networks 280 7.4 Adaptive Evolutionary Games on Networks 284 References 286 8 Network Synchronization 289 8.1 Introduction 289 8.2 Complete Synchronization of Continuous-Time Networks 290 8.2.1 Complete Synchronization of General Continuous-Time Networks 293 8.2.2 Complete Synchronization of Linearly Coupled Continuous-Time Networks 297 8.3 Complete Synchronization of Some Typical Dynamical Networks 299 8.3.1 Complete Synchronization of Regular Networks 300 8.3.2 Synchronization of Small-World Networks 301 8.3.3 Synchronization of Scale-Free Networks 302 8.3.4 Complete Synchronization of Local-World Networks 306 8.4 Phase Synchronization 306 8.4.1 Phase Synchronization of the Kuramoto Model 308 8.4.2 Phase Synchronization of Small-World Networks 310 8.4.3 Phase Synchronization of Scale-Free Networks 310 8.4.4 Phase Synchronization of Nonuniformly Coupled Networks 314 References 316 9 Network Control 319 9.1 Introduction 319 9.2 Spatiotemporal Chaos Control on Regular CML 319 9.3 Pinning Control of Complex Networks 322 9.3.1 Augmented Network Approach 322 9.3.2 Pinning Control of Scale-Free Networks 323 9.4 Pinning Control of General Complex Networks 326 9.4.1 Stability Analysis of General Networks under Pinning Control 326 9.4.2 Pinning and Virtual Control of General Networks 328 9.4.3 Pinning and Virtual Control of Scale-Free Networks 330 9.5 Time-Delay Pinning Control of Complex Networks 333 9.6 Consensus and Flocking Control 335 References 340 10 Brief Introduction to Other Topics 343 10.1 Human Opinion Dynamics 343 10.2 Human Mobility and Behavioral Dynamics 346 10.3 Web PageRank, SiteRank and BrowserRank 348 10.3.1 Methods Based on Edge Analysis 348 10.3.2 Methods Using Users’ Behavior Data 348 10.4 Recommendation Systems 349 10.5 Network Edge Prediction 350 10.6 Living Organisms and Bionetworks 351 10.7 Cascading Reactions on Networks 353 References 356 Index 363

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Book SynopsisPraise for the First Edition This pioneering work, in which Rao provides a comprehensive and up-to-date treatment of small area estimation, will become a classic...I believe that it has the potential to turn small area estimation...into a larger area of importance to both researchers and practitioners.Journal of the American Statistical Association Written by two experts in the field, Small Area Estimation, Second Edition provides a comprehensive and up-to-date account of the methods and theory of small area estimation (SAE), particularly indirect estimation based on explicit small area linking models. The model-based approach to small area estimation offers several advantages including increased precision, the derivation of optimal estimates and associated measures of variability under an assumed model, and the validation of models from the sample data. Emphasizing real data throughout, the Second Edition maintaiTrade Review"The book is an excellent reference for practicing statisticians and survey methodologists as well as practitioners interested in learning SAE methods. The second edition is also an ideal textbook for graduate-level courses in SAE and reliable small area statistics." (Zentralblatt MATH, 2016)Table of ContentsList of Figures xv List of Tables xvii Foreword to the First Edition xix Preface to the Second Edition xxiii Preface to the First Edition xxvii 1 *Introduction 1 1.1 What is a Small Area? 1 1.2 Demand for Small Area Statistics 3 1.3 Traditional Indirect Estimators 4 1.4 Small Area Models 4 1.5 Model-Based Estimation 5 1.6 Some Examples 6 1.6.1 Health 6 1.6.2 Agriculture 7 1.6.3 Income for Small Places 8 1.6.4 Poverty Counts 8 1.6.5 Median Income of Four-Person Families 8 1.6.6 Poverty Mapping 8 2 Direct Domain Estimation 9 2.1 Introduction 9 2.2 Design-Based Approach 10 2.3 Estimation of Totals 11 2.3.1 Design-Unbiased Estimator 11 2.3.2 Generalized Regression Estimator 13 2.4 Domain Estimation 16 2.4.1 Case of No Auxiliary Information 16 2.4.2 GREG Domain Estimation 17 2.4.3 Domain-Specific Auxiliary Information 18 2.5 Modified GREG Estimator 21 2.6 Design Issues 23 2.6.1 Minimization of Clustering 24 2.6.2 Stratification 24 2.6.3 Sample Allocation 24 2.6.4 Integration of Surveys 25 2.6.5 Dual-Frame Surveys 25 2.6.6 Repeated Surveys 26 2.7 *Optimal Sample Allocation for Planned Domains 26 2.7.1 Case (i) 26 2.7.2 Case (ii) 29 2.7.3 Two-Way Stratification: Balanced Sampling 31 2.8 Proofs 32 2.8.1 Proof of ŶGR(𝐱) = 𝐗 32 2.8.2 Derivation of Calibration Weights 𝑤∗j 32 2.8.3 Proof of Y = X^T𝐁^when cj = 𝝂T𝐗j 32 3 Indirect Domain Estimation 35 3.1 Introduction 35 3.2 Synthetic Estimation 36 3.2.1 No Auxiliary Information 36 3.2.2 *Area Level Auxiliary Information 36 3.2.3 *Unit Level Auxiliary Information 37 3.2.4 Regression-Adjusted Synthetic Estimator 42 3.2.5 Estimation of MSE 43 3.2.6 Structure Preserving Estimation 45 3.2.7 *Generalized SPREE 49 3.2.8 *Weight-Sharing Methods 53 3.3 Composite Estimation 57 3.3.1 Optimal Estimator 57 3.3.2 Sample-Size-Dependent Estimators 59 3.4 James–Stein Method 63 3.4.1 Common Weight 63 3.4.2 Equal Variances 𝜓i = 𝜓 64 3.4.3 Estimation of Component MSE 68 3.4.4 Unequal Variances 𝜓i 70 3.4.5 Extensions 71 3.5 Proofs 71 4 Small Area Models 75 4.1 Introduction 75 4.2 Basic Area Level Model 76 4.3 Basic Unit Level Model 78 4.4 Extensions: Area Level Models 81 4.4.1 Multivariate Fay–Herriot Model 81 4.4.2 Model with Correlated Sampling Errors 82 4.4.3 Time Series and Cross-Sectional Models 83 4.4.4 *Spatial Models 86 4.4.5 Two-Fold Subarea Level Models 88 4.5 Extensions: Unit Level Models 88 4.5.1 Multivariate Nested Error Regression Model 88 4.5.2 Two-Fold Nested Error Regression Model 89 4.5.3 Two-Level Model 90 4.5.4 General Linear Mixed Model 91 4.6 Generalized Linear Mixed Models 92 4.6.1 Logistic Mixed Models 92 4.6.2 *Models for Multinomial Counts 93 4.6.3 Models for Mortality and Disease Rates 93 4.6.4 Natural Exponential Family Models 94 4.6.5 *Semi-parametric Mixed Models 95 5 Empirical Best Linear Unbiased Prediction (EBLUP): Theory 97 5.1 Introduction 97 5.2 General Linear Mixed Model 98 5.2.1 BLUP Estimator 98 5.2.2 MSE of BLUP 100 5.2.3 EBLUP Estimator 101 5.2.4 ML and REML Estimators 102 5.2.5 MSE of EBLUP 105 5.2.6 Estimation of MSE of EBLUP 106 5.3 Block Diagonal Covariance Structure 108 5.3.1 EBLUP Estimator 108 5.3.2 Estimation of MSE 109 5.3.3 Extension to Multidimensional Area Parameters 110 5.4 *Model Identification and Checking 111 5.4.1 Variable Selection 111 5.4.2 Model Diagnostics 114 5.5 *Software 118 5.6 Proofs 119 5.6.1 Derivation of BLUP 119 5.6.2 Equivalence of BLUP and Best Predictor E(𝐦T𝐯|𝐀T𝐲) 120 5.6.3 Derivation of MSE Decomposition (5.2.29) 121 6 Empirical Best Linear Unbiased Prediction (EBLUP): Basic Area Level Model 123 6.1 EBLUP Estimation 123 6.1.1 BLUP Estimator 124 6.1.2 Estimation of 𝜎2𝑣 126 6.1.3 Relative Efficiency of Estimators of 𝜎2𝑣 128 6.1.4 *Applications 129 6.2 MSE Estimation 136 6.2.1 Unconditional MSE of EBLUP 136 6.2.2 MSE for Nonsampled Areas 139 6.2.3 *MSE Estimation for Small Area Means 140 6.2.4 *Bootstrap MSE Estimation 141 6.2.5 *MSE of a Weighted Estimator 143 6.2.6 Mean Cross Product Error of Two Estimators 144 6.2.7 *Conditional MSE 144 6.3 *Robust Estimation in the Presence of Outliers 146 6.4 *Practical Issues 148 6.4.1 Unknown Sampling Error Variances 148 6.4.2 Strictly Positive Estimators of 𝜎2𝑣 151 6.4.3 Preliminary Test Estimation 154 6.4.4 Covariates Subject to Sampling Errors 156 6.4.5 Big Data Covariates 159 6.4.6 Benchmarking Methods 159 6.4.7 Misspecified Linking Model 165 6.5 *Software 169 7 Basic Unit Level Model 173 7.1 EBLUP Estimation 173 7.1.1 BLUP Estimator 174 7.1.2 Estimation of 𝜎2𝑣 and 𝜎2e 177 7.1.3 *Nonnegligible Sampling Fractions 178 7.2 MSE Estimation 179 7.2.1 Unconditional MSE of EBLUP 179 7.2.2 Unconditional MSE Estimators 181 7.2.3 *MSE Estimation: Nonnegligible Sampling Fractions 182 7.2.4 *Bootstrap MSE Estimation 183 7.3 *Applications 186 7.4 *Outlier Robust EBLUP Estimation 193 7.4.1 Estimation of Area Means 193 7.4.2 MSE Estimation 198 7.4.3 Simulation Results 199 7.5 *M-Quantile Regression 200 7.6 *Practical Issues 205 7.6.1 Unknown Heteroscedastic Error Variances 205 7.6.2 Pseudo-EBLUP Estimation 206 7.6.3 Informative Sampling 211 7.6.4 Measurement Error in Area-Level Covariate 216 7.6.5 Model Misspecification 218 7.6.6 Semi-parametric Nested Error Model: EBLUP 220 7.6.7 Semi-parametric Nested Error Model: REBLUP 224 7.7 *Software 227 7.8 *Proofs 231 7.8.1 Derivation of (7.6.17) 231 7.8.2 Proof of (7.6.20) 232 8 EBLUP: Extensions 235 8.1 *Multivariate Fay–Herriot Model 235 8.2 Correlated Sampling Errors 237 8.3 Time Series and Cross-Sectional Models 240 8.3.1 *Rao–Yu Model 240 8.3.2 State-Space Models 243 8.4 *Spatial Models 248 8.5 *Two-Fold Subarea Level Models 251 8.6 *Multivariate Nested Error Regression Model 253 8.7 Two-Fold Nested Error Regression Model 254 8.8 *Two-Level Model 259 8.9 *Models for Multinomial Counts 261 8.10 *EBLUP for Vectors of Area Proportions 262 8.11 *Software 264 9 Empirical Bayes (EB) Method 269 9.1 Introduction 269 9.2 Basic Area Level Model 270 9.2.1 EB Estimator 271 9.2.2 MSE Estimation 273 9.2.3 Approximation to Posterior Variance 275 9.2.4 *EB Confidence Intervals 281 9.3 Linear Mixed Models 287 9.3.1 EB Estimation of 𝜇i = 𝐥iT𝜷 + 𝐦Ti 𝐯i 287 9.3.2 MSE Estimation 288 9.3.3 Approximations to the Posterior Variance 288 9.4 *EB Estimation of General Finite Population Parameters 289 9.4.1 BP Estimator Under a Finite Population 290 9.4.2 EB Estimation Under the Basic Unit Level Model 290 9.4.3 FGT Poverty Measures 293 9.4.4 Parametric Bootstrap for MSE Estimation 294 9.4.5 ELL Estimation 295 9.4.6 Simulation Experiments 296 9.5 Binary Data 298 9.5.1 *Case of No Covariates 299 9.5.2 Models with Covariates 304 9.6 Disease Mapping 308 9.6.1 Poisson–Gamma Model 309 9.6.2 Log-Normal Models 310 9.6.3 Extensions 312 9.7 *Design-Weighted EB Estimation: Exponential Family Models 313 9.8 Triple-Goal Estimation 315 9.8.1 Constrained EB 316 9.8.2 Histogram 318 9.8.3 Ranks 318 9.9 Empirical Linear Bayes 319 9.9.1 LB Estimation 319 9.9.2 Posterior Linearity 322 9.10 Constrained LB 324 9.11 *Software 325 9.12 Proofs 330 9.12.1 Proof of (9.2.11) 330 9.12.2 Proof of (9.2.30) 330 9.12.3 Proof of (9.8.6) 331 9.12.4 Proof of (9.9.1) 331 10 Hierarchical Bayes (HB) Method 333 10.1 Introduction 333 10.2 MCMC Methods 335 10.2.1 Markov Chain 335 10.2.2 Gibbs Sampler 336 10.2.3 M–H Within Gibbs 336 10.2.4 Posterior Quantities 337 10.2.5 Practical Issues 339 10.2.6 Model Determination 342 10.3 Basic Area Level Model 347 10.3.1 Known 𝜎2𝑣 347 10.3.2 *Unknown 𝜎2𝑣: Numerical Integration 348 10.3.3 Unknown 𝜎2𝑣: Gibbs Sampling 351 10.3.4 *Unknown Sampling Variances 𝜓i 354 10.3.5 *Spatial Model 355 10.4 *Unmatched Sampling and Linking Area Level Models 356 10.5 Basic Unit Level Model 362 10.5.1 Known 𝜎2𝑣 and 𝜎2e 362 10.5.2 Unknown 𝜎2𝑣 and 𝜎2e: Numerical Integration 363 10.5.3 Unknown 𝜎2𝑣 and 𝜎2e: Gibbs Sampling 364 10.5.4 Pseudo-HB Estimation 365 10.6 General ANOVA Model 368 10.7 *HB Estimation of General Finite Population Parameters 369 10.7.1 HB Estimator under a Finite Population 370 10.7.2 Reparameterized Basic Unit Level Model 370 10.7.3 HB Estimator of a General Area Parameter 372 10.8 Two-Level Models 374 10.9 Time Series and Cross-Sectional Models 377 10.10 Multivariate Models 381 10.10.1 Area Level Model 381 10.10.2 Unit Level Model 382 10.11 Disease Mapping Models 383 10.11.1 Poisson-Gamma Model 383 10.11.2 Log-Normal Model 384 10.11.3 Two-Level Models 386 10.12 *Two-Part Nested Error Model 388 10.13 Binary Data 389 10.13.1 Beta-Binomial Model 389 10.13.2 Logit-Normal Model 390 10.13.3 Logistic Linear Mixed Models 393 10.14 *Missing Binary Data 397 10.15 Natural Exponential Family Models 398 10.16 Constrained HB 399 10.17 *Approximate HB Inference and Data Cloning 400 10.18 Proofs 402 10.18.1 Proof of (10.2.26) 402 10.18.2 Proof of (10.2.32) 402 10.18.3 Proof of (10.3.13)–(10.3.15) 402 References 405 Author Index 431 Subject Index 437

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Book SynopsisIntroduction to Statistical Analysis of Laboratory Data presents a detailed discussion of important statistical concepts and methods of data presentation and analysis Provides detailed discussions on statistical applications including a comprehensive package of statistical tools that are specific to the laboratory experiment process Introduces terminology used in many applications such as the interpretation of assay design and validation as well as fit for purpose procedures including real world examples Includes a rigorous review of statistical quality control procedures in laboratory methodologies and influences on capabilities Presents methodologies used in the areas such as method comparison procedures, limit and bias detection, outlier analysis and detecting sources of variation Analysis of robustness and ruggedness including multivariate influences on response are introduced to account for controllable/uncontrollable laboraTrade Review"The book presents a detailed discussion of important statistical concepts and methods of data presentation and analysis. -Provides detailed discussions on statistical applications including a comprehensive package of statistical tools that are specific to the laboratory experiment process. - Introduces terminology used in many applications such as the interpretation of assay design and validation as well as fit for purpose" procedures including real world examples." (Zentralblatt MATH 2016)Table of ContentsPreface xi Acknowledgments xv 1 Descriptive Statistics 1 1.1 Measures of Central Tendency 1 1.2 Measures of Variation 4 1.3 Laboratory Example 7 1.4 Putting it All Together 8 1.5 Summary 10 References 10 2 Distributions and Hypothesis Testing in Formal Statistical Laboratory Procedures 11 2.1 Introduction 11 2.2 Confidence Intervals (CT) 19 2.2.1 Confidence Interval (CI) for the Population Mean – The t-Distribution 20 2.2.2 Confidence Interval for the Variance and Standard Deviation 21 2.3 Inferential Statistics – Hypothesis Testing 23 2.3.1 t-Test for Means 25 2.3.2 Test for Variation: Coefficient of Variation (CV) 28 2.3.3 Two-Sample Test of the Population Means 29 2.3.4 One-Way Analysis of Variance (ANOVA) 34 2.3.5 Nonparametric Tests for Skewed Data 40 References 41 3 Method Validation 43 3.1 Introduction 43 3.2 Accuracy 45 3.2.1 Method 1 45 3.2.2 Method 2 56 3.3 Brief Introduction to Bioassay 59 3.3.1 Direct Assay 59 3.3.2 Indirect Assay 61 3.4 Sensitivity, Specificity (Selectivity) 69 3.5 Method Validation and Method Agreement – Bland-Altman 73 References 76 4 Methodologies in Outlier Analysis 79 4.1 Introduction 79 4.2 Some Outlier Determination Techniques 80 4.2.1 Grubb Statistic 82 4.2.2 Other Forms of the Grubb Statistic 84 4.2.3 Studentized Range Statistic 85 4.2.4 Sequential Test of Many Outliers 86 4.2.5 Mahalanobis Distance Measure 88 4.2.6 Dixon Q-Test for a Single Outlier 91 4.2.7 The Box Plot 94 4.2.8 Median Absolute Deviation 95 4.3 Combined Method Comparison Outlier Analysis 96 4.3.1 Further Outlier Considerations 96 4.3.2 Combined Method Comparison Outlier Analysis – Refined Method Comparisons Using Bland – Altman 98 4.4 Some Consequences of Outlier Removal 103 4.5 Considering Outlier Variance 104 4.5.1 The Cochran C test 104 4.5.2 Cochran G Test 107 References 110 5 Statistical Process Control 113 5.1 Introduction 113 5.2 Control Charts 115 5.2.1 Means (X-bar) Control Charts 117 5.2.2 Range Control Charts 122 5.2.3 The S-Chart 124 5.2.4 The Median Chart 126 5.2.5 Mean (X-bar) and S-Charts Based on the Median Absolute Deviation (MAD) 128 5.3 Capability Analysis 131 5.4 Capability Analysis – An Alternative Consideration 137 References 139 6 Limits of Calibration 141 6.1 Calibration: Limit Strategies for Laboratory Assay Data 141 6.1.1 Definition – Calibration 141 6.2 Limit Strategies 142 6.2.1 Example – Estimation of LoB and LoD for Drug Assay 142 6.2.2 LoQ Results 144 6.2.3 A Comparison of Empirical and Statistical Approaches to the LoD and LoQ 145 6.2.4 Example – LoD/LoQ, GC – MS Approach 145 6.2.5 LoD/LoQ, GC – MS Approach 146 6.2.6 Explanation of the Difficulty of the Statistical Methodology for the LoD and LoQ 147 6.2.7 Another LoQ Method 151 6.3 Method Detection Limits (EPA) 151 6.3.1 Method Detection Limits 151 6.3.2 Example – Atrazine by Gas Chromatography (GC) 152 6.3.3 LoD and LoQ Summary 153 6.4 Data Near the Detection Limits 154 6.4.1 Biased Estimators 154 6.4.2 Computing Some Statistics with the LoD in the Data 154 6.5 More on Statistical Management of Nondetects 156 6.5.1 Model-Based Examples of Measuring Nondetects 157 6.5.2 An Alternative Regression Approach with Improvements (Refer to the Box Cox Transformation in Chapter 5) 160 6.5.3 Extension of the ROS Method for Multiple NDs in Various Positions 163 6.5.4 Cohen’s Adjustment 165 6.6 The Kaplan – Meier Method (Nonparametric Approach) for Analysis of Laboratory Data with Nondetects 170 References 174 7 Calibration Bias 177 7.1 Error 177 7.1.1 Types of Error 179 7.2 Uncertainty 180 7.3 Sources of Uncertainty 180 7.4 Estimation Methods of Uncertainty 181 7.4.1 Statistical Estimation Methods of Type A Uncertainty 181 7.4.2 Estimation Methods of Type B Uncertainty 183 7.4.3 Estimation Methods of Combined and Expanded Uncertainties (Normal Data) 187 7.4.4 Estimation Methods of Combined and Expanded Uncertainties (Nonnormal Data) 190 7.4.5 Another Method of Estimating Uncertainties for Nonnormal Data (Nonparametric) 192 7.5 Calibration Bias 194 7.5.1 Gas Chromatographic/Mass Spectrometric (GC – MS) Calibration Bias 197 7.5.2 Discussion 205 7.6 Multiple Instruments 205 7.7 Crude Versus Precise Methodologies 208 References 210 8 Robustness and Ruggedness 213 8.1 Introduction 213 8.2 Robustness 214 8.3 Ruggedness 216 8.4 An Alternative Procedure for Ruggedness Determination 224 8.5 Ruggedness and System Suitability Tests 227 8.5.1 Determining the SST Limits from Replicated Experimentation 228 8.5.2 Determining the SST Limits from Statistical Prediction 231 References 233 Index 235

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Book SynopsisVolume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshevpolynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition;conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities toexplore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussTable of ContentsList of Symbols xiii Preface xv 31. Fibonacci and Lucas Polynomials I 1 31.1. Fibonacci and Lucas Polynomials 3 31.2. Pascal’s Triangle 18 31.3. Additional Explicit Formulas 22 31.4. Ends of the Numbers ln 25 31.5. Generating Functions 26 31.6. Pell and Pell–Lucas Polynomials 27 31.7. Composition of Lucas Polynomials 33 31.8. De Moivre-like Formulas 35 31.9. Fibonacci–Lucas Bridges 36 31.10. Applications of Identity (31.51) 37 31.11. Infinite Products 48 31.12. Putnam Delight Revisited 51 31.13. Infinite Simple Continued Fraction 54 32. Fibonacci and Lucas Polynomials II 65 32.1. Q-Matrix 65 32.2. Summation Formulas 67 32.3. Addition Formulas 71 32.4. A Recurrence for n2 76 32.5. Divisibility Properties 82 33. Combinatorial Models II 87 33.1. A Model for Fibonacci Polynomials 87 33.2. Breakability 99 33.3. A Ladder Model 101 33.4. A Model for Pell–Lucas Polynomials: Linear Boards 102 33.5. Colored Tilings 103 33.6. A New Tiling Scheme 104 33.7. A Model for Pell–Lucas Polynomials: Circular Boards 107 33.8. A Domino Model for Fibonacci Polynomials 114 33.9. Another Model for Fibonacci Polynomials 118 34. Graph-Theoretic Models II 125 34.1. Q-Matrix and Connected Graph 125 34.2. Weighted Paths 126 34.3. Q-Matrix Revisited 127 34.4. Byproducts of the Model 128 34.5. A Bijection Algorithm 136 34.6. Fibonacci and Lucas Sums 137 34.7. Fibonacci Walks 140 35. Gibonacci Polynomials 145 35.1. Gibonacci Polynomials 145 35.2. Differences of Gibonacci Products 159 35.3. Generalized Lucas and Ginsburg Identities 174 35.4. Gibonacci and Geometry 181 35.5. Additional Recurrences 184 35.6. Pythagorean Triples 188 36. Gibonacci Sums 195 36.1. Gibonacci Sums 195 36.2. Weighted Sums 206 36.3. Exponential Generating Functions 209 36.4. Infinite Gibonacci Sums 215 37. Additional Gibonacci Delights 233 37.1. Some Fundamental Identities Revisited 233 37.2. Lucas and Ginsburg Identities Revisited 238 37.3. Fibonomial Coefficients 247 37.4. Gibonomial Coefficients 250 37.5. Additional Identities 260 37.6. Strazdins’ Identity 264 38. Fibonacci and Lucas Polynomials III 269 38.1. Seiffert’s Formulas 270 38.2. Additional Formulas 294 38.3. Legendre Polynomials 314 39. Gibonacci Determinants 321 39.1. A Circulant Determinant 321 39.2. A Hybrid Determinant 323 39.3. Basin’s Determinant 333 39.4. Lower Hessenberg Matrices 339 39.5. Determinant with a Prescribed First Row 343 40. Fibonometry II 347 40.1. Fibonometric Results 347 40.2. Hyperbolic Functions 356 40.3. Inverse Hyperbolic Summation Formulas 361 41. Chebyshev Polynomials 371 41.1. Chebyshev Polynomials Tn(x) 372 41.2. Tn(x) and Trigonometry 384 41.3. Hidden Treasures in Table 41.1 386 41.4. Chebyshev Polynomials Un(x) 396 41.5. Pell’s Equation 398 41.6. Un(x) and Trigonometry 399 41.7. Addition and Cassini-like Formulas 401 41.8. Hidden Treasures in Table 41.8 402 41.9. A Chebyshev Bridge 404 41.10. Tn and Un as Products 405 41.11. Generating Functions 410 42. Chebyshev Tilings 415 42.1. Combinatorial Models for Un 415 42.2. Combinatorial Models for Tn 420 42.3. Circular Tilings 425 43. Bivariate Gibonacci Family I 429 43.1. Bivariate Gibonacci Polynomials 429 43.2. Bivariate Fibonacci and Lucas Identities 430 43.3. Candido’s Identity Revisited 439 44. Jacobsthal Family 443 44.1. Jacobsthal Family 444 44.2. Jacobsthal Occurrences 450 44.3. Jacobsthal Compositions 452 44.4. Triangular Numbers in the Family 459 44.5. Formal Languages 468 44.6. A USA Olympiad Delight 480 44.7. A Story of 1, 2, 7, 42, 429,…483 44.8. Convolutions 490 45. Jacobsthal Tilings and Graphs 499 45.1. 1 × n Tilings 499 45.2. 2 × n Tilings 505 45.3. 2 × n Tubular Tilings 510 45.4. 3 × n Tilings 514 45.5. Graph-Theoretic Models 518 45.6. Digraph Models 522 46. Bivariate Tiling Models 537 46.1. A Model for 𝑓n(x, y) 537 46.2. Breakability 539 46.3. Colored Tilings 542 46.4. A Model for ln(x, y) 543 46.5. Colored Tilings Revisited 545 46.6. Circular Tilings Again 547 47. Vieta Polynomials 553 47.1. Vieta Polynomials 554 47.2. Aurifeuille’s Identity 567 47.3. Vieta–Chebyshev Bridges 572 47.4. Jacobsthal–Chebyshev Links 573 47.5. Two Charming Vieta Identities 574 47.6. Tiling Models for Vn 576 47.7. Tiling Models for 𝑣n(x) 582 48. Bivariate Gibonacci Family II 591 48.1. Bivariate Identities 591 48.2. Additional Bivariate Identities 594 48.3. A Bivariate Lucas Counterpart 599 48.4. A Summation Formula for 𝑓2n(x, y) 600 48.5. A Summation Formula for l2n(x, y) 602 48.6. Bivariate Fibonacci Links 603 48.7. Bivariate Lucas Links 606 49. Tribonacci Polynomials 611 49.1. Tribonacci Numbers 611 49.2. Compositions with Summands 1, 2, and 3 613 49.3. Tribonacci Polynomials 616 49.4. A Combinatorial Model 618 49.5. Tribonacci Polynomials and the Q-Matrix 624 49.6. Tribonacci Walks 625 49.7. A Bijection between the Two Models 627 Appendix 631 A.1. The First 100 Fibonacci and Lucas Numbers 631 A.2. The First 100 Pell and Pell–Lucas Numbers 634 A.3. The First 100 Jacobsthal and Jacobsthal–Lucas Numbers 638 A.4. The First 100 Tribonacci Numbers 642 Abbreviations 644 Bibliography 645 Solutions to Odd-Numbered Exercises 661 Index 725

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Book SynopsisPraise for the First Edition beautiful and well worth the reading with many exercises and a good bibliography, this book will fascinate both students and teachers.Table of Contents1 Leonardo Fibonacci 9 2 Fibonacci Numbers 13 2.1 Fibonacci's Rabbits 13 2.2 Fibonacci Numbers 14 2.3 Fibonacci and Lucas Curiosities 17 3 Fibonacci Numbers in Nature 27 3.1 Fibonacci, Flowers, and Trees 28 3.2 Fibonacci and Male Bees 31 3.3 Fibonacci, Lucas, and Subsets 32 3.4 Fibonacci and Sewage Treatment 34 3.5 Fibonacci and Atoms 35 3.6 Fibonacci and Reflections 36 3.7 Paraffins and Cycloparaffins 38 3.8 Fibonacci and Music 41 3.9 Fibonacci and Poetry 42 3.10 Fibonacci and Neurophysiology 43 3.11 Electrical Networks 45 4 Additional Fibonacci and Lucas Occurrences 53 4.1 Fibonacci Occurrences 53 4.2 Fibonacci and Compositions 58 4.3 Fibonacci and Permutations 61 4.4 Fibonacci and Generating Sets 63 4.5 Fibonacci and Graph Theory 64 4.6 Fibonacci Walks 66 4.7 Fibonacci Trees 68 4.8 Partitions 71 4.9 Fibonacci and the Stock Market 72 5 Fibonacci and Lucas Identities 77 5.1 Spanning Tree of a Connected Graph 79 5.2 Binet's Formulas 83 5.3 Cyclic Permutations and Lucas Numbers 91 5.4 Compositions Revisited 94 5.5 Number of Digits in Fn and Ln 94 5.6 Theorem 5.8 Revisited 95 5.7 Catalan's Identity 99 5.8 Additional Fibonacci and Lucas Identities 102 5.9 Fermat and Fibonacci 108 5.10 Fibonacci and 110 6 Geometric Illustrations and Paradoxes 117 6.1 Geometric Illustrations 117 6.2 Candido's Identity 121 6.3 Fibonacci Tessellations 123 6.4 Lucas Tessellations 123 6.5 Geometric Paradoxes 124 6.6 Cassini-Based Paradoxes 124 6.7 Additional Paradoxes 129 7 Gibonacci Numbers 133 7.1 Gibonacci Numbers 133 7.2 Germain's Identity 139 8 Additional Fibonacci and Lucas Formulas 145 8.1 New Explicit Formulas 145 8.2 Additional Formulas 148 9 The Euclidean Algorithm 159 9.1 The Euclidean Algorithm 160 9.2 Formula (5.5) Revisited 162 9.3 Lamé's Theorem 164 10 Divisibility Properties 167 10.1 Fibonacci Divisibility 167 10.2 Lucas Divisibility 173 10.3 Fibonacci and Lucas Ratios 173 10.4 An Altered Fibonacci Sequence 178 11 Pascal's Triangle 185 11.1 Binomial Coefficients 185 11.2 Pascal's Triangle 186 11.3 Fibonacci Numbers and Pascal’s Triangle 188 11.4 Another Explicit Formula for Ln 191 11.5 Catalan's Formula 192 11.6 Additional Identities 192 11.7 Fibonacci Paths of a Rook on a Chessboard 194 12 Pascal-like Triangles 199 12.1 Sums of Like-Powers 199 12.2 An Alternate Formula for Ln 202 12.3 Differences of Like-Powers 202 12.4 Catalan's Formula Revisited 204 12.5 A Lucas Triangle 205 12.6 Powers of Lucas Numbers 209 12.7 Variants of Pascal's Triangle 211 13 Recurrences and Generating Functions 219 13.1 LHRWCCs 219 13.2 Generating Functions 223 13.3 A Generating Function For F3n 233 13.4 A Generating Function For F3 n 234 13.5 Summation Formula (5.1) Revisited 234 13.6 A List of Generating Functions 235 13.7 Compositions Revisited 238 13.8 Exponential Generating Functions 239 13.9 Hybrid Identities 241 13.10Identities Using the Differential Operator 242 14 Combinatorial Models I 249 14.1 A Fibonacci Tiling Model 249 14.2 A Circular Tiling Model 255 14.3 Path Graphs Revisited 259 14.4 Cycle Graphs Revisited 262 14.5 Tadpole Graphs 263 15 Hosoya's Triangle 271 15.1 Recursive Definition 271 15.2 A Magic Rhombus 273 16 The Golden Ratio 279 16.1 Ratios of Consecutive Fibonacci Numbers 279 16.2 The Golden Ratio 281 16.3 Golden Ratio as Nested Radicals 285 16.4 Newton's Approximation Method 286 16.5 The Ubiquitous Golden Ratio 288 16.6 Human Body and the Golden Ratio 289 16.7 Violin and the Golden Ratio 290 16.8 Ancient Floor Mosaics and the Golden Ratio 290 16.9 Golden Ratio in an Electrical Network 290 16.10Golden Ratio in Electrostatics 291 16.11Golden Ratio by Origami 292 16.12Differential Equations 297 16.13Golden Ratio in Algebra 299 16.14Golden Ratio in Geometry 300 17 Golden Triangles and Rectangles 309 17.1 Golden Triangle 309 17.2 Golden Rectangles 314 17.3 The Parthenon 317 17.4 Human Body and the Golden Rectangle 318 17.5 Golden Rectangle and the Clock 319 17.6 Straightedge and Compass Construction 320 17.7 Reciprocal of a Rectangle 321 17.8 Logarithmic Spiral 322 17.9 Golden Rectangle Revisited 324 17.10Supergolden Rectangle 324 18 Figeometry 329 18.1 The Golden Ratio and Plane Geometry 329 18.2 The Cross of Lorraine 335 18.3 Fibonacci Meets Appollonius 337 18.4 A Fibonacci Spiral 338 18.5 Regular Pentagons 339 18.6 Trigonometric Formulas for Fn 343 18.7 Regular Decagon 347 18.8 Fifth Roots of Unity 348 18.9 A Pentagonal Arch 351 18.10 Regular Icosahedron and Dodecahedron 351 18.11 Golden Ellipse 352 18.12 Golden Hyperbola 354 19 Continued Fractions 361 19.1 Finite Continued Fractions 361 19.2 Convergents of a Continued Fraction 364 19.3 Infinite Continued Fractions 366 19.4 A Nonlinear Diophantine Equation 368 20 Fibonacci Matrices 371 20.1 The Q-Matrix 371 20.2 Eigenvalues of Qn 378 20.3 Fibonacci and Lucas Vectors 384 20.4 An Intriguing Fibonacci Matrix 386 20.5 An Infinite-Dimensional Lucas Matrix 391 20.6 An Infinite-Dimensional Gibonacci Matrix 397 20.7 The Lambda Function 398 21 Graph-theoretic Models I 407 21.1 A Graph-theoretic Model for Fibonacci Numbers 407 21.2 Byproducts of the Combinatorial Models 409 21.3 Summation Formulas 415 22 Fibonacci Determinants 419 22.1 An Application to Graph Theory 419 22.2 The Singularity of Fibonacci Matrices 425 22.3 Fibonacci and Analytic Geometry 427 23 Fibonacci and Lucas Congruences 437 23.1 Fibonacci Numbers Ending in Zero 437 23.2 Lucas Numbers Ending in Zero 437 23.3 Additional Congruences 438 23.4 Lucas Squares 439 23.5 Fibonacci Squares 440 23.6 A Generalized Fibonacci Congruence 442 23.7 Fibonacci and Lucas Periodicities 449 23.8 Lucas Squares Revisited 450 23.9 Periodicities Modulo 10n 452 24 Fibonacci and Lucas Series 461 24.1 A Fibonacci Series 461 24.2 A Lucas Series 463 24.3 Fibonacci and Lucas Series Revisited 464 24.4 A Fibonacci Power Series 467 24.5 Gibonacci Series 472 24.6 Additional Fibonacci Series 474 25 Weighted Fibonacci and Lucas Sums 481 25.1 Weighted Sums 481 25.2 Gauthier's Differential Method 488 26 Fibonometry I 495 26.1 Golden Ratio and Inverse Trigonometric Functions 495 26.2 Golden Triangle Revisited 496 26.3 Golden Weaves 497 26.4 Additional Fibonometric Bridges 498 26.5 Fibonacci and Lucas Factorizations 504 27 Completeness Theorems 509 27.1 Completeness Theorem 509 27.2 Egyptian Algorithm for Multiplication 510 28 The Knapsack Problem 513 28.1 The Knapsack Problem 513 29 Fibonacci and Lucas Subscripts 517 29.1 Fibonacci and Lucas Subscripts 517 29.2 Gibonacci Subscripts 519 29.3 A Recursive Definition of Yn 520 30 Fibonacci and the Complex Plane 525 30.1 Gaussian Numbers 525 30.2 Gaussian Fibonacci and Lucas Numbers 526 30.3 Analytic Extensions 530 1 A.1 Fundamentals 537 SOLUTIONS TO ODD-NUMBERED EXERCISES 575

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