Probability and statistics Books

Book SynopsisAims to provides applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).Trade ReviewFrom the reviews: "This book presents a wealth of results on Young measures on topological spaces in a very general framework. It is very likely that it will become the reference and starting point for any further developments in the field." (Georg K. Dolzmann, Mathematical Reviews, 2005k)Table of ContentsPreface. Generalities, Preliminary results. Young Measures, the four Stable Topologies: S, M, N, W. Convergence in Probability of Young Measures (with some applications to stable convergence). Compactness. Strong Tightness. Young Measures on Banach Spaces. Application. Applications in Control Theory. Semicontinuity of Integral Functionals using Young Measures. Stable Convergence in Limit Theorems of Probability Theory.

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Book SynopsisIn this revised and enlarged second edition, Tony Guénault provides a clear and refreshingly readable introduction to statistical physics. The treatment itself is self-contained and concentrates on an understanding of the physical ideas, without requiring a high level of mathematical sophistication.Trade ReviewFrom the reviews of the second edition: "This is an introductory level textbook on the basics of statistical physics. … it is an easy-to-read textbook, suited for bachelor students who want to learn the basics of statistical physics by themselves." (Jacques Tempere, Physicalia Magazine, Vol. 30 (4), 2008)Table of ContentsPreface 1: Basic Ideas. 1.1. The Macrostate. 1.2. Microstates. 1.3. The Average Postulate. 1.4. Distributions. 1.5. The Statistical method in Outline. 1.6. A Model Example. 1.7. Statistical Entropy and Microstates. 1.8 Summary. 2: Distinguishable Particles. 2.1. The Thermal Equilibrium Distribution. 2.2. What are a and ß? 2.3. A Statistical Definition of Temperature. 2.4. The Boltzman Distribution and the Partition Function. 2.5. Calculation of Thermodynamic Functions. 2.6. Summary. 3: Two Examples. 3.1. A spin-½ Solid. 3.2. Localized harmonic Oscillators. 3.3. Summary. 4: Gases: The Density of States. 4.1. Fitting waves into boxes. 4.2. Other Information for Statistical Physics. 4.3. An Example – Helium Gas. 4.4. Summary 5: Gases: The Distributions. 5.1. Distribution in groups. 5.2. Identical Particles – Fermions and Bosons. 5.3. Counting Microstates for Gases. 5.4. The Three Distributions. 5.5. Summary. 6: Maxwell-Boltzmann Gases. 6.1. The validity of the Maxwell-Boltzmann Limit. 6.2. The Maxwell-Boltzmann Distribution of Speeds. 6.3. The Connection to Thermodynamics. 6.4. Summary. 7: Diatomic Gases. 7.1. Energy Contributions in Diatomic Gases. 7.2. Heat Capacity of a Diatomic Gas. 7.3. The Heat Capacity of Hydrogen. 7.4. Summary. 8: Fermi-Dirac Gases. 8.1. Properties of an Ideal Fermi-Dirac Gas. 8.2. Application to Metals. 8.3. Application to Helium-3. 8.4. Summary. 9: Bose-Einstein Gases. 9.1. Properties of an Ideal Bose-Einstein Gas. 9.2. Application to Helium-4. 9.3. Phoney Bosons. 9.4. A Note about Cold Atoms. 9.5. Summary. 10: Entropy in Other Situations. 10.1. Entropy and Disorder. 10.2. An Assembly at Fixed Temperature. 10.3. Vacancies in Solids. 11: Phase Transitions. 11.1. Types of Phase Transition. 11.2. Ferromagnetism of a spin-½ Solid. 11.3. Real Ferromagnetic Materials. 11.4. Order-Disorder Transformations in Alloys. 12: Two New Ideas. 12.1. Statistics or Dynamics. 12.2. Ensembles – a LargerView. 13: Chemical Thermodynamics. 13.1. Chemical Potential Revisited. 13.2. The Grand Canonical Ensemble. 13.3. Ideal Gases in the Grand Ensemble. 13.4. Mixed Systems and Chemical Reactions. 14: Dealing with Interactions. 14.1. Electrons in Metals. 14.2. Liquid Helium-3: a Fermi Liquid. 14.3. Liquid Helium-4: a Bose Liquid? 14.4. Real Imperfect Gases. 15: Statistics under Extreme Conditions. 15.1. Superfluid States in Fermi-Dirac Systems. 15.2. Statistics in Astrophysical Systems. Appendix A – Some Elementary Counting Problems Appendix B – Some Problems with Large Numbers Appendix C – Some Useful Integrals Appendix D – Some Useful Constants Appendix E – Exercises Appendix F – Answers to Exercises Index

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Book SynopsisSuitable for anyone working with problems of linear and nonlinear least squares fitting, this book includes an overview of computational methods together with their properties and advantages. It also includes topics from statistical regression analysis that help readers to understand and evaluate the computed solutions.Trade ReviewLeast Square Data fitting with Applications is a book that will be of great practical use to anyone whose work involves the analysis of data and its modeling. It offers a great deal of information that can be a s valuable in the lecture theater as in the lab or office. Mathematics TodayTable of ContentsPrefaceSymbols and AcronymsChapter 1. The Linear Data Fitting Problem1.1. Parameter estimation, data approximation1.2. Formulation of the data fitting problem1.3. Maximum likelihood estimation1.4. The residuals and their properties1.5. Robust regressionChapter 2. The Linear Least Squares Problem2.1. Linear least squares problem formulation2.2. The QR factorization and its role2.3. Permuted QR factorizationChapter 3. Analysis of Least Squares Problems3.1. The pseudoinverse3.2. The singular value decomposition3.3. Generalized singular value decomposition3.4. Condition number and column scaling3.5. Perturbation analysisChapter 4. Direct Methods for Full-Rank Problems4.1. Normal equations4.2. LU factorization4.3. QR factorization4.4. Modifying least squares problems4.5. Iterative refinement4.6. Stability and condition number estimation4.7. Comparison of the methodsChapter 5. Direct Methods for Rank-Deficient Problems5.1. Numerical rank5.2. Peters-Wilkinson LU factorization5.3. QR factorization with column permutations5.4. UTV and VSV decompositions5.5. Bidiagonalization5.6. SVD computationsChapter 6. Methods for Large-Scale Problems6.1. Iterative versus direct methods6.2. Classical stationary methods6.3. Non-stationary methods, Krylov methods6.4. Practicalities: preconditioning and stopping criteria6.5. Block methodsChapter 7. Additional Topics in Least Squares7.1. Constrained linear least squares problems7.2. Missing data problems7.3. Total least squares (TLS)7.4. Convex optimization7.5. Compressed sensingChapter 8. Nonlinear Least Squares Problems8.1. Introduction8.2. Unconstrained problems8.3. Optimality conditions for constrained problems8.4. Separable nonlinear least squares problems8.5. Multiobjective optimizationChapter 9. Algorithms for Solving Nonlinear LSQ Problems9.1. Newton's method9.2. The Gauss-Newton method9.3. The Levenberg-Marquardt method9.4. Additional considerations and software9.5. Iteratively reweighted LSQ algorithms for robust data fitting problems9.6. Variable projection algorithm9.7. Block methods for large-scale problemsChapter 10. Ill-Conditioned Problems10.1. Characterization10.2. Regularization methods10.3. Parameter selection techniques10.4. Extensions of Tikhonov regularization10.5. Ill-conditioned NLLSQ problemsChapter 11. Linear Least Squares Applications11.1. Splines in approximation11.2. Global temperatures data fitting11.3. Geological surface modelingChapter 12. Nonlinear Least Squares Applications12.1. Neural networks training12.2. Response surfaces, surrogates or proxies12.3. Optimal design of a supersonic aircraft12.4. NMR spectroscopy12.5. Piezoelectric crystal identification12.6. Travel time inversion of seismic dataAppendix A: Sensitivity AnalysisA.1. Floating-point arithmeticA.2. Stability, conditioning and accuracyAppendix B: Linear Algebra BackgroundB.1. NormsB.2. Condition numberB.3. OrthogonalityB.4. Some additional matrix propertiesAppendix C: Advanced Calculus BackgroundC.1. Convergence ratesC.2. Multivariable calculusAppendix D: StatisticsD.1. DefinitionsD.2. Hypothesis testingReferencesIndex

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Book SynopsisNumerical Exploration.- Batches of Numbers.- The Level or Center of a Batch.- The Spread or Dispersion of a Batch.- Comparing Batches.- The Shape or Distribution of a Batch.- Categories.- Sampling.- Samples and Populations.- Different Samples from the Same Population.- Confidence and Population Means.- Medians and Resampling.- Categories and Population Proportions.- Relationships between Two Variables.- Comparing Two Sample Means.- Comparing Means of More than Two Samples.- Comparing Proportions of Different Samples.- Relating a Measurement Variable to Another Measurement Variable.- Relating Ranks.- Special Topics in Sampling.- Sampling a Population with Subgroups.- Sampling a Site or Region with Spatial Units.- Sampling without Finding Anything.- Sampling and Reality.- Multivariate Analysis.- Multivariate Approaches and Variables.- Similarities between Cases.- Multidimensional Scaling.- Principal Components Analysis.- Cluster Analysis.Trade ReviewPraise for the 2nd Edition:"Statistics is often perceived as something mysterious and hostile, and this holds particularly true for archaeologists... The merit of Drennan's work is that he takes readers by the hand and gently guides them through that minefield, etting them discover that statistics can be a matter easily approached and understood from a commonsense perspective...Fourteen years after the first edition, a number of important new topics are added. They provide the reader with useful tools to explore archaeological data as the data becomes progressively multivariate...Each section uses the same case study and data set, thus enhancing the comparability of this technique...Drennan successfully conveys complex concepts in smple ways...both students and scholars will surely welcome this gentle introduction to statistics, wherein simplicity does not detract from scientific precision". (Gianmarco Alberti, American Journal of Archaeology, 114.4, 2010)."this is a superb book, setting the use of basic statistics in a format that makes sense of the formulas rather than just saying "compute this". Mathematically fluent students who scorn a specific context will complain that there is too much "talky talky" surrounding the formulas. That talk, missing from many applied elementary statistics, is especially what the audience for this book needs and deserves, and rarely gets in class, in my experience...Robert Drennan [has]...succeeded where others have failed, namely to explain, in an understandable way, the advantages of simple statistical techniques in a specific applied context. I heartily recommend this title." (Norman R. Draper, International Statistical Review, 79.1, 2011). Praise for the first edition:“Robert Drennan has done the field a great service.” (Larry R. Kimball, American Antiquity, Vol 62 (1997)"There is a great deal to recommend this book.... It is written in an engaging style...and it is consistently focused on the practical problems of archaeological analysis." (Robert E. Dewar, SAS Bulletin, July 1997)"...this book is highly recommended." (Gary Lock, American Journal of Archaeology, Vol 101 (1997)"I will use this book when I teach statistics in the future, and I will gladly recommend it to others." (Randall McGuire, Historical Archaeology, Vol 32 (1998)"an excellent introductory textbook ...introducing complex ideas on statistics to students in a practical, non-threatening way.... [It] will help us to train our students to be better consumers of the statistical analyses they must deal with throughout their careers." (Mark Aldendorfer, Journal of Field Archaeology, Vol 25 (1998)“Robert Drennan has done the field a great service.” (American Antiquity)“Statistics for Archaeologists effectively integrates both traditional statistical methods and more recent techniques of exploratory data analysis (EDA)...One of the major strengths of this book is its emphasis on sampling...Drennan has produced a usable and insightful statistics text.” (Journal of Field Archaeology, 1998)Table of ContentsNumerical Exploration: 1. Batches of Numbers (Stemandleaf Plots, Histograms). 2. The Level, or Center, of a Batch (Mean and Median). 3. The Spread or Dispersion of a Batch (Range, Midspread, and Standard Deviation). 4. Comparing Batches (The BoxandDot Plot). 5. The Shape or Distribution of a Batch (Symmetry and Transformations). 6. Categories (Column and Row Proportions) Random Sampling: 7. Samples and Populations (Randomness and Sampling Bias). 8. Different Samples from the Same Population (Variation, the `Special Batch', and Standard Error). 9. Confidence and Population Means (Precision and Error Ranges, Student's t, Determining How Large of a Sample Is Needed). 10. Categories and Population Proportions (Percentages Instead of Means) Relationships between Two Variables: 11. Comparing Two Sample Means (The t Test, Results and Interpretations). 12. Comparing Means of More than Two Samples (Relating a Categorical Variable to a Measurement Variable, Analysis of Variance). 13. Comparing Proportions of Different Samples (Relating a Categorical Variable to Another Categorical Variable, Chisquare). 14. Relating a Measurement Variable to Another Measurement Variable. 15. Relating Ranks. 16. Sampling a Population with Subgroups. 17. Sampling a Site or Region with Spatial Units. 18. Sampling without Finding Anything. 19. Sampling and Reality Suggested Reading. Index.

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Book SynopsisA.- Acceptance Region.- Accuracy.- Algorithm.- Alternative hypothesis.- Analysis of binary data.- Analysis of categorical data.- Analysis of residuals.- Analysis of variance.- Anderson Oskar.- Anderson Theodore W.- Anderson-Darling test.- Arithmetic mean.- Arithmetic triangle.- ARMA models.- Arrangement.- Attributable risk.- Autocorrelation and partial autocorrelation.- Avoidable risk.Trade ReviewFrom the reviews: "This book claims to concentrate ‘on the most important topics’ (of Statistics) and explain those ‘as deeply as space has allowed’. … in general, the book is quite easy to read, and the cross-references are useful. … In all, it is a useful reference that should be found in many academic and corporate libraries." (Kimmo Vehkalahti, International Statistical Review, Vol. 76 (3), 2008) "The aim has been to provide a short and concise encyclopaedia for those who do not wish to purchase any of the several large or multi-volume encyclopaedias in the field. … I am inclined to see this as a library reference book for most scientists. Practising statisticians, particularly those teaching, will probably find this a useful reference book with its original references … worked through mathematical aspects and worked examples." (John Goodier, Reference Reviews, Vol. 23 (2), 2009)Table of ContentsA.- Acceptance Region.- Accuracy.- Algorithm.- Alternative hypothesis.- Analysis of binary data.- Analysis of categorical data.- Analysis of residuals.- Analysis of variance.- Anderson Oskar.- Anderson Theodore W.- Anderson-Darling test.- Arithmetic mean.- Arithmetic triangle.- ARMA models.- Arrangement.- Attributable risk.- Autocorrelation and partial autocorrelation.- Avoidable risk.

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Book SynopsisBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.Trade ReviewFrom the reviews:“Robert and Casella’s new book uses the programming language R, a favorite amongst (Bayesian) statisticians to introduce in eight chapters both basic and advanced Monte Carlo techniques … . The book could be used as the basic textbook for a semester long course on computational statistics with emphasis on Monte Carlo tools … . useful for (and should be next to the computer of) a large body of hands on graduate students, researchers, instructors and practitioners … .” (Hedibert Freitas Lopes, Journal of the American Statistical Association, Vol. 106 (493), March, 2011)“Chapters focuses on MCMC methods the Metropolis–Hastings algorithm, Gibbs sampling, and monitoring and adaptation for MCMC algorithms. … There are exercises within and at the end of all chapters … . Overall, the level of the book makes it suitable for graduate students and researchers. Others who wish to implement Monte Carlo methods, particularly MCMC methods for Bayesian analysis will also find it useful.” (David Scott, International Statistical Review, Vol. 78 (3), 2010)“The primary audience is graduate students in statistics, biostatistics, engineering, etc. who need to know how to utilize Monte Carlo simulation methods to analyze their experiments and/or datasets. … this text does an effective job of including a selection of Monte Carlo methods and their application to a broad array of simulation problems. … Anyone who is an avid R user and has need to integrate and/or optimize complex functions will find this text to be a necessary addition to his or her personal library.” (Dean V. Neubauer, Technometrics, Vol. 53 (2), May, 2011)Table of ContentsBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.

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Book SynopsisUnivariate Distributions.- Bivariate Copulas.- Distributions Expressed as Copulas.- Concepts of Stochastic Dependence.- Measures of Dependence.- Construction of Bivariate Distributions.- Bivariate Distributions Constructed by the Conditional Approach.- Variables-in-Common Method.- Bivariate Gamma and Related Distributions.- Simple Forms of the Bivariate Density Function.- Bivariate Exponential and Related Distributions.- Bivariate Normal Distribution.- Bivariate Extreme-Value Distributions.- Elliptically Symmetric Bivariate Distributions and Other Symmetric Distributions.- Simulation of Bivariate Observations.Trade ReviewFrom the reviews of the second edition:“The authors present the forms, properties, dependence structures, computation, and applications of numerous continuous bivariate distributions. … One of the nice features of this edition is that it presents bivariate distributions that are generated by a variety of copulas. … The new edition is comprised of 14 chapters including references at the end of each chapter … and subject index at the end. … I can safely recommend this book as a handy resource manual for researchers as well as practitioners working in this area.” (Technometrics, Vol. 51 (4), November, 2009)“The book begins with a survey of univariate distributions, necessary to clarify notation in subsequent chapters. … Every time you open this volume, even at a random page, you’ll likely find something of interest. … You might well recommend it as collateral reading in a statistics class that you are teaching. As the students progress in their academic pursuits and/or in their subsequent careers, it will be a useful reference.” (Barry C. Arnold, Mathematical Reviews, Issue 2012 h)Table of ContentsUnivariate distributions. - Bivariate copulas. - Distributions expressed as copulas. - Concepts of stochastic dependence. - Measures of dependence. - Constructions of bivariate distributions.- Bivariate distributions constructed by conditional approach. - Variables in common method. - Bivariate gamma and related distributions. - Simple forms of the bivariate density function. - Bivariate exponentional and related distributions. - Bivariate normal distribution. - Bivariate extreme value distributions. - Elliptically symmetric bivariate distributions and other symmetric distributions. - Simulation of bivariate observations.

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Book SynopsisPricing by Arbitrage.- Martingale Measures.- The First Fundamental Theorem.- Complete Markets.- Discrete-time American Options.- Continuous-Time Stochastic Calculus.- Continuous-Time European Options.- The American Put Option.- Bonds and Term Structure.- Consumption-Investment Strategies.- Measures of Risk.Trade ReviewFrom the reviews: "...This book is a valuable addition to a graduate student's reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." SIAM Review, December 2005 From the reviews of the second edition: "The book is very carefully formatted. … this book is a valuable addition to a graduate student’s reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." (Alexandre D’Aspremont, SIAM Reviews, December, 2005) "The emphasis of the first edition of this book was on developing the mathematical concepts for the rapidly expanding field of mathematical finance. This second edition contains a significant number of changes and additions … . The target audience is readers with sound mathematical background on elementary concepts from measure-theoretic probability … . It should be an equally valuable resource to practitioners interested in the mathematical tools … . will be a very useful addition to any scholarly library." (Theofanis Sapatinas, Journal of Applied Sciences, Vol. 32 (6), 2005) "The second edition adds new matieral from current active research areas. A new chapter on coherent risk measures for instance reflects the recent trend in research and applications in the area of risk management. In summary, this is an excellent textbook in mathematical finance, and I can definitely recommend it." (S. Peng, Short Book Reviews of the ISI, June 2006)Table of ContentsPricing by Arbitrage * Martingale Measures * The Fundamental Theorem of Asset Pricing * Complete Markets and Martingale Representation * Stopping Times and American Options * A Review of Continuous Time Stochastic Calculus * European Options in Continuous Time * The American Option * Bonds and Term Structure * Consumption-Investment Strategies *

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Book SynopsisThis text provides the reader with a single book where they can find accounts of a number of up-to-date issues in nonparametric inference. The book is aimed at Masters or PhD level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. It covers a wide range of topics including the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book's dual approach includes a mixture of methodology and theory.Trade ReviewFrom the reviews: "...The book is excellent." (Short Book Reviews of the ISI, June 2006) "Now we have All of Nonparametric Statistics … the writing is excellent and the author is to be congratulated on the clarity achieved. … the book is excellent." (N.R. Draper, Short Book Reviews, 26:1, 2006) "Overall, I enjoyed reading this book very much. I like Wasserman's intuitive explanations and careful insights into why one path or approach is taken over another. Most of all, I am impressed with the wealth of information on the subject of asymptotic nonparametric inferences." (Stergios B. Fotopoulos for Technometrics, 49:1, February 2007) "The intention of this book is to give a single source with brief accounts of modern topics in nonparametric inference. … The text is a mixture of theory and applications, and there are lots of examples … . The text is also illustrated with many informative figures. … this book covers many topics of modern nonparametric methods, with focus on estimation and on the construction of confidence sets. It should be a useful reference for anyone interested in the theories and methods of this area." (Andreas Karlsson, Statistical Papers, 48, 2006) "...ANPS provides an excellent complement or a complete course textbook with a mixture of theoretical and computational exercises. ...For a book in a rapidly evolving field, the content and references are quit eup to date. ...As advertised, it offers a well-written, albeit brief account of numerous topics in modern nonparametric inference." (Greg Ridgeway, Journal of the American Statistical Association, Vol. 102, No. 477, 2007) "This is a nicely written textbook oriented mainly to master level statistics and computer science students. The author provides wide a coverage of modern nonparametric methods … . the key ideas and basic proofs are carefully explained. Bibliographic remarks point the reader to references that contain further details. Each chapter is finished with useful exercises … . The book is also suitable for researchers in statistics, machine learning, and data mining." (Oleksandr Kukush, Zentralblatt MATH, Vol. 1099 (1), 2007)Table of ContentsEstimating the CDF and Statistical Functionals.- The Bootstrap and the Jackknife.- Smoothing: General Concepts.- Nonparametric Regression.- Density Estimation.- Normal Means and Minimax Theory.- Nonparametric Inference Using Orthogonal Functions.- Wavelets and Other Adaptive Methods.- Other Topics.

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Book Synopsis1 Set.- 1.1 Sample sets.- 1.2 Operations with sets.- 1.3 Various relations.- 1.4 Indicator.- Exercises.- 2 Probability.- 2.1 Examples of probability.- 2.2 Definition and illustrations.- 2.3 Deductions from the axioms.- 2.4 Independent events.- 2.5 Arithmetical density.- Exercises.- 3 Counting.- 3.1 Fundamental rule.- 3.2 Diverse ways of sampling.- 3.3 Allocation models; binomial coefficients.- 3.4 How to solve it.- Exercises.- 4 Random Variables.- 4.1 What is a random variable?.- 4.2 How do random variables come about?.- 4.3 Distribution and expectation.- 4.4 Integer-valued random variables.- 4.5 Random variables with densities.- 4.6 General case.- Exercises.- Appendix 1: Borel Fields and General Random Variables.- 5 Conditioning and Independence.- 5.1 Examples of conditioning.- 5.2 Basic formulas.- 5.3 Sequential sampling.- 5.4 Pólya's urn scheme.- 5.5 Independence and relevance.- 5.6 Genetical models.- Exercises.- 6 Mean, Variance, and Transforms.- 6.1 Basic properties of expectationTrade Review"In spite of the original edition of the book being nearly thirty years old, the text still has its role to play in first and second year undergraduate probability courses. It provides an excellent foundation to more advanced courses in the subject."Short Book Reviews, Vol. 23/3, Dec. 2003 "This edition is the third revision of a text on mathematical probability first published in 1974. The text is aimed at undergraduate mathematics students and is accessible to a general audience. The prose is accurate, entertaining, and dense with historical tidbits. Two concluding chapters on mathematical finance have been added to the eight chapters in the third edition by the second author." The American Statistician, May 2004 From the reviews of the fourth edition: "The main novelty in the fourth edition of this well-written book is the addition of new chapters … . The new chapters share the friendly yet rigorous style of the former ones. They begin with an account of the financial vocabulary, which is then expounded in probabilistic terms. … Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." (Ricardo Maronna, Statistical Papers, Vol. 45 (4), 2004)Table of ContentsSet * Probability * Counting * Random Variables * Conditioning and Independence * Mean, Variance and Transforms * Poisson and Normal Distributions * From Random Walks to Markov Chains * Mean-Variance Pricing Model * Option Pricing Theory

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Book SynopsisGetting Started.- The Normal Curve and Outlier Detection.- Accuracy and Inference.- Hypothesis Testing and Small Sample Sizes.- The Bootstrap.- A Fundamental Problem.- Robust Measures of Location.- Inferences About Robust Measures of Location.- Measures Of Association.- Robust Regression.- Alternative Strategies and Software.Trade ReviewFrom the reviews of the second edition:“It is a well-written and neatly organized book that introduces modern robust statistical methods … . the book not only a handbook for applied researchers who need to conduct reasonable and interpretable data analysis, but also a good textbook for non-statistics students and statistics undergraduate students. This is the only book on the subject written for this audience to my knowledge. … It provides insights and more methodological options in statistical analysis for students and applied researchers.”­­­ (Tian Siva Tian, Psychometrika, Vol. 76 (1), January, 2011)Table of ContentsPart One: Genesis of a Science*Derivation Curve*What Am I Holding*Least Squares*Quantifying Accuracy*Solving Bernoulli's Problem*Promoting Normality*Part II Exploiting Normality*Dealing with Small Samples Sizes*Correlation*Part Three: Dealing with Nonnormality*Revolution with a Whimper*Robust Methods*Bootstrap *Conclusion

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Book SynopsisMultivariate data and multivariate analysis.- Looking at multivariate data: visualization.- Principal components analysis.- Multidimensional scaling.-Exploratory factor analysis.- Cluster analysis.- Confirmatory factor analysis and structural equation models.- The analysis of repeated measures data.-Trade Review“This book covers basic to advanced approaches for the analysis of multivariate data in R. … All chapters end with a summary and exercises, making this book an excellent addition to applied statistics courses. The approach, numerous examples and fragments of code make it accessible to undergraduate and postgraduate students alike, as well as researchers … .” (Irina Ioana Mohorianu, zbMATH 1306.62010, 2015)“Each chapter introduces briefly the theory on well-known methods to analyze multivariate data and then focuses on the application of the multivariate techniques to example data with R. … addressed to students in applied statistics courses or applied statisticians looking for a valuable educational textbook on multivariate analysis. … an ideal textbook for students or persons, employed in the field of applied statistics, who wish to study the analysis of multivariate data and to apply multivariate techniques to real data.” (Wiebke Werft, Biometrical Journal, Vol. 55 (6), 2013)“This practical book provides a well-organized summary of popular multivariate data analysis techniques with practical examples. As the book title indicates, all introduced techniques are accompanied by relevant and friendly R codes, and thus it can be used for excellent R programming reference for those who wish to use R for multivariate data analysis.” (Technometrics, Vol. 54 (4), November, 2012)Table of ContentsMultivariate data and multivariate analysis.- Looking at multivariate data: visualization.- Principal components analysis.- Multidimensional scaling.- Exploratory factor analysis.- Cluster analysis.- Confirmatory factor analysis and structural equation models.- The analysis of repeated measures data.-

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Book SynopsisParts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.Trade ReviewFrom the reviews:“This book is a timely fit and is expected to draw much attention from researchers in the field of causal inference. The book explains the concept of targeted learning, which is an enhanced procedure for estimating targeted causal estimands under the potential outcome framework. … Excellent summaries of complex estimation procedures and methods are ubiquitous, which will be helpful for the nontechnical readers of the book. … This book appears to be a useful reference for Ph.D. students in biostatistics programs.” (Joseph Kang, Journal of the American Statistical Association, June, 2013)Table of ContentsModels, Inference, and Truth.- The Open Problem.- Defining the Model and Parameter.- Super Learning.- Introduction to TMLE.- Understanding TMLE.- Why TMLE?.- Bounded Continuous Outcomes.- Direct Effects and Effect Among the Treated.- Marginal Structural Models.- Positivity.- Robust Analysis of RCTs Using Generalized Linear Models.- Targeted ANCOVA Estimator in RCTs.- Independent Case-Control Studies.- Why Match? Matched Case-Control Studies.- Nested Case-Control Risk Score Prediction.- Super Learning for Right-Censored Data.- RCTs with Time-to-Event Outcomes.- RCTs with Time-to-Event Outcomes and Effect Modification Parameters.- C-TMLE of an Additive Point Treatment Effect.- C-TMLE for Time-to-Event Outcomes.- Propensity-Score-Based Estimators and C-TMLE.- Targeted Methods for Biomarker Discovery.- Finding Quantitative Trait Loci Genes.- Case Study: Longitudinal HIV Cohort Data.- Probability of Success of an In Vitro Fertilization Program.- Individualized Antiretroviral Initiation Rules.- Cross-Validated Targeted Minimum-Loss-Based Estimation.- Targeted Bayesian Learning.- TMLE in Adaptive Group Sequential Covariate Adjusted RCTs.- Foundations of TMLE.- Introduction to R Code Implementation.

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Book Synopsis1 Basic Concepts and Elementary Models.- 1. The Vocabulary of Probability Theory.- 2. Events and Probability.- 3. Random Variables and Their Distributions.- 4. Conditional Probability and Independence.- 5. Solving Elementary Problems.- 6. Counting and Probability.- 7. Concrete Probability Spaces.- Illustration 1. A Simple Model in Genetics: Mendel's Law and HardyWeinberg's Theorem.- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle.- Illustration 3. Bertrand's Paradox.- 2 Discrete Probability.- 1. Discrete Random Elements.- 2. Variance and Chebyshev's Inequality.- 3. Generating Functions.- Illustration 4. An Introduction to Population Theory: GaltonWatson's Branching Process.- Illustration 5. Shannon's Source Coding Theorem: An Introduction to Information Theory.- 3 Probability Densities.- I. Expectation of Random Variables with a Density.- 2. Expectation of Functionals of Random Vectors.- 3. Independence.- 4. Random Variables That Are Not Discrete anTable of Contents1 Basic Concepts and Elementary Models.- 1. The Vocabulary of Probability Theory.- 2. Events and Probability.- 2.1. Probability Space.- 2.2. Two Elementary Probabilistic Models.- 3. Random Variables and Their Distributions.- 3.1. Random Variables.- 3.2. Cumulative Distribution Function.- 4. Conditional Probability and Independence.- 4.1. Independence of Events.- 4.2. Independence of Random Variables.- 5. Solving Elementary Problems.- 5.1. More Formulas.- 5.2. A Small Bestiary of Exercises.- 6. Counting and Probability.- 7. Concrete Probability Spaces.- Illustration 1. A Simple Model in Genetics: Mendel’s Law and Hardy—Weinberg’s Theorem.- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle.- Illustration 3. Bertrand’s Paradox.- 2 Discrete Probability.- 1. Discrete Random Elements.- 1.1. Discrete Probability Distributions.- 1.2. Expectation.- 1.3. Independence.- 2. Variance and Chebyshev’s Inequality.- 2.1. Mean and Variance.- 2.2. Chebyshev’s Inequality.- 3. Generating Functions.- 3.1. Definition and Basic Properties.- 3.2. Independence and Product of Generating Functions.- Illustration 4. An Introduction to Population Theory: Galton—Watson’s Branching Process.- Illustration 5. Shannon’s Source Coding Theorem: An Introduction to Information Theory.- 3 Probability Densities.- I. Expectation of Random Variables with a Density.- 1.1. Univariate Probability Densities.- 1.2. Mean and Variance.- 1.3. Chebyshev’s Inequality.- 1.4. Characteristic Function of a Random Variable.- 2. Expectation of Functionals of Random Vectors.- 2.1. Multivariate Probability Densities.- 2.2. Covariance, Cross-Covariance, and Correlation.- 2.3. Characteristic Function of a Random Vector.- 3. Independence.- 3.1. Independent Random Variables.- 3.2. Independent Random Vectors.- 4. Random Variables That Are Not Discrete and Do Not Have a pd.- 4.1. The Abstract Definition of Expectation.- 4.2. Lebesgue’s Theorems and Applications.- Illustration 6. Buffon’s Needle: A Problem in Random Geometry.- 4 Gauss and Poisson.- 1. Smooth Change of Variables.- 1.1. The Method of the Dummy Function.- 1.2. Examples.- 2. Gaussian Vectors.- 2.1. Characteristic Function of Gaussian Vectors.- 2.2. Probability Density of a Nondegenerate Gaussian Vector.- 2.3. Moments of a Centered Gaussian Vector.- 2.4. Random Variables Related to Gaussian Vectors.- 3. Poisson Processes.- 3.1. Homogeneous Poisson Processes Over the Positive Half Line.- 3.2. Nonhomogeneous Poisson Processes Over the Positive Half Line.- 3.3. Homogeneous Poisson Processes on the Plane.- 4. Gaussian Stochastic Processes.- 4.1. Stochastic Processes and Their Law.- 4.2. Gaussian Stochastic Processes.- Illustration 7. An Introduction to Bayesian Decision Theory: Tests of Gaussian Hypotheses.- 5 Convergences.- 1. Almost-Sure Convergence.- 1.1. The Borel—Cantelli Lemma.- 1.2. A Criterion for Almost-Sure Convergence.- 1.3. The Strong Law of Large Numbers.- 2. Convergence in Law.- 2.1. Criterion of the Characteristic Function.- 2.2. The Central Limit Theorem.- 3. The Hierarchy of Convergences.- 3.1. Almost-Sure Convergence Versus Convergence in Probability.- 3.2. Convergence in the Quadratic Mean.- 3.3. Convergence in Law in the Hierarchy of Convergences.- 3.4. The Hierarchical Tableau.- Illustration 8. A Statistical Procedure: The Chi-Square Test.- Illustration 9. Introduction to Signal Theory: Filtering.- Additional Exercises.- Solutions to Additional Exercises.

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Book SynopsisThe Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Environment.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Environment.- Combinatorics.- Economics.- Integer Optimization.Trade ReviewFrom the reviews:“In an effort at reform, Hurlbert (Arizona State) dubs his subject ‘linear optimization’ … . the author designs his work for discovery-based learning. … Ideally, this volume offers students the opportunity to recapitulate the Socratic process for reinforcement … . Summing Up: Recommended. Lower-division undergraduates.” (D. V. Feldman, Choice, Vol. 47 (9), May, 2010)“Hurlbert’s textbook focuses on the mathematics of linear programming and important connections to linear algebra, graph theory, convexity, and game theory. The author has adopted the Moore method in which students are given some basic terminology and definitions and are then asked to develop the subject by proving a series of theorems. … This textbook would be very suitable for an undergraduate course in linear programming that uses the Moore method.” (Brian Borchers, The Mathematical Association of America, February, 2010)“This text is … oriented toward duality as central to solving and understanding linear optimization problems. … Sequential steps in the ‘Workouts’ help guide the student through the discovery process. … this book would be an excellent choice for an instructor wishing to teach linear optimization to a motivated class. There is enough in here to sustain every taste and approach and create an excellent first course in optimization.” (Steven R. Dunbar, SIAM Review, Vol. 53 (3), 2011)Table of ContentsIntroduction.- The Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Implementation.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Implementation.- Combinatorics.- Economics.- Integer Optimization.- Appendix A: Linear Algebra Overview.- Appendix B: The Equivalence of the Auxiliary and Shortcut Methods.- Appendix C: Complexity.- Appendix D: LOP Catalog.

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Book SynopsisThis study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950.Trade ReviewFrom the book reviews:“Fischer provides thorough mathematical descriptions of the development of the central limit theorem as it evolves with increasing mathematical rigor. … Fischer has probably written what will be the definitive history of the central limit theorem for many years to come. … Fischer overflows with detail, insight and excellent commentary.” (David Bellhouse, Historia Mathematica, Vol. 39, 2012)“The book will be of interest not only to professionals in the area of probability and statistics but to a wider audience. … The author has been using a huge amount of sources and archives, including his own works, and he is successful in his goal to describe a comprehensive picture of the development of the CLT. … the book would be an excellent source for student projects on topics from probability and its applications.” (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1226, 2012)“This work details the history of the central limit theorem and related probabilistic limit theorems roughly from 1810 through 1950, but focuses on 1810 to 1935. … Hans Fischer … authors many papers on the history of mathematics. His skill in both these areas allows him to reveal here the historical development of this important theorem in a way that can easy be adapted to the lecture hall or used in independent study.” (Tom Schulte, The Mathematical Association of America, February, 2011)“The history of the CLT deserves a place of its own, and this book by Hans Fischer is the best … in tracing its development in meticulous historical detail and with mathematical precision. … The book by Hans Fischer is highly recommended as a well-researched comprehensive history of the CLT. One finds here the story of a galaxy of brilliant mathematicians … engaging in the quest for, and debates on, the true meaning and the correct derivation of a beautiful intriguing result.”­­­ (Rabi Bhattacharya, SIAM Review, Vol. 53 (4), 2011)Table of ContentsPreface.- Introduction.- The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods.- The hypothesis of elementary errors.- Chebyshev's and markov's contributions.- The way towards modern probability.- General limit problems.- Conclusion: the central limit theorem as a link between classical and modern probability.- Index.- Bibliography

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Book SynopsisContinual improvements in data collection and processing have had a huge impact on brain research, producing data sets that are often large and complicated. By demonstrating the commonality among various statistical approaches the authors provide the crucial tools for gaining knowledge from diverse types of data.Trade ReviewThis is an outstanding book, that fills a real need. Assuming no background in statistics, it covers the data analysis methods neuroscientists need to know, from standard material like hypothesis tests, to specialized methods that have recently found use in our field. It has the detail and insight needed for those developing their own statistical methods. And for the working neurobiologist it has plenty of practical tricks, tips, and examples, coming straight from the experts. This book is a must for anyone serious about quantitative analysis in neuroscience. Kenneth D. Harris, Professor of Quantitative Neuroscience, University College London Analysis of Neural Data is a thorough, authoritative textbook on the fastest growing statistical field. All relevant topics are covered in depth with examples from the literature and thoughtful comments. Particularly welcome is the discussion of multivariate statistics, time series and Bayesian methods, topics frequently encountered in neuroscience research but infrequently discussed in standard statistics textbooks. A highly readable, useful and commendable textbook! Apostolos P. Georgopoulos, Regents Professor of Neuroscience, University of Minnesota This book is a unique and valuable resource for any scientist who wants to approach neural data analysis in a rigorous fashion, or to gain a broad overview of modern statistical concepts and approaches. While the book is an eminently practical guide, it is far from a cookbook. The individual who is willing to invest the time to read it will be deeply rewarded not only with everyday methodological guidance, but also, with a comprehensive understanding of the mathematical foundations of statistics. The first chapter, in which the authors lucidly present a perspective on what statistics has to offer, should be required reading for all neuroscientists - or at least, all who care about data. The authors have met the difficult and competing challenges of creating a book that is both practical and rigorous. To do this, they combine a crisp writing style with a number of helpful strategies, including the use of many carefully-chosen examples from the neuroscience literature, and vivid reminders of the difference between the world of mathematical objects and the world of data. Mathematical concepts that are typically omitted from elementary texts are not avoided, but are discussed in a way that makes their relevance evident...The book is a one-of-a-kind resource that combines practicality, rigor, and accessibility; it is a book that was sorely needed and is an extremely valuable reference. Jonathan D. Victor, Fred Plum Professor, Brain and Mind Research Institute and Department of Neurology, Weill Cornell Medical College Analysis of Neural Data provides an invaluable guide for neuroscientists seeking to summarize and interpret their data. The authors -- leading statisticians who have developed and applied many of the methods they describe themselves - are also outstanding teachers, and the treatment they provide is at once accessible, authoritative, comprehensive, and up-to-date. The book provides a carefully structured introduction to statistical methods for students at the beginning of their research careers as well as a treatment of several advanced methods that will be of value to practicing researchers. James L. McClelland, Lucie Stern Professor in the Social Sciences, Director, Center for Mind, Brain and Computation, Stanford University Written by eminent statisticians, this book covers a range of topics from basic mathematics to state-of-the-art statistical analyses of neural data. Researchers conducting experiments will learn the principles of data analysis and will begin analyzing data using the methods provided. Theoreticians will be introduced to more than 100 intriguing experiments that will teach them to form persuasive interpretations. Analysis of Neural Data should become a standard reference for neuroscience research. Shigeru Shinomoto, Department of Physics, Kyoto UniversityTable of ContentsIntroduction.- Exploring Data.- Probability and Random Variables.- Random Vectors.- Important Probability Distributions.- Sequences of Random Variables.- Estimation and Uncertainty.- Estimation in Theory and Practice.- Uncertainty and the Bootstrap.- Statistical Significance.- General Methods for Testing Hypotheses.- Linear Regression.- Analysis of Variance.- Generalized Regression.- Nonparametric Regression.- Bayesian Methods.- Multivariate Analysis.- Time Series.- Point Processes.- Appendix: Mathematical Background.- Example Index.- Index.- Bibliography.

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Table of Contents1. Anatomy of a Function2. Inside a Function-Call3. Expressions and Environments4. Manipulating Expressions 5. Working with Substitutions

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Book SynopsisIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups.Trade ReviewFrom the book reviews:“This textbook provides a comprehensive and consistent introduction to measure and integration theory. … The book can be recommended to anyone having basic knowledge of calculus and point-set topology. It is very self-contained, and can thus serve as an excellent reference book as well.” (Ville Suomala, Mathematical Reviews, July, 2014)“In this second edition, Cohn has updated his excellent introduction to measure theory … and has made this great textbook even better. Those readers unfamiliar with Cohn’s style will discover that his writing is lucid. … this is a wonderful text to learn measure theory from and I strongly recommend it.” (Tushar Das, MAA Reviews, June, 2014)Table of Contents1. Measures.- Algebras and sigma-algebras.- Measures.- Outer measures.- Lebesgue measure.- Completeness and regularity.- Dynkin classes.- 2. Functions and Integrals.- Measurable functions.- Properties that hold almost everywhere.- The integral.- Limit theorems.- The Riemann integral.- Measurable functions again, complex-valued functions, and image measures.- 3. Convergence.- Modes of Convergence.- Normed spaces.- Definition of L^p and L^p.- Properties of L^p and L-p.- Dual spaces.- 4. Signed and Complex Measures.- Signed and complex measures.- Absolute continuity.- Singularity.- Functions of bounded variation.- The duals of the L^p spaces.- 5. Product Measures.- Constructions.- Fubini’s theorem.- Applications.- 6. Differentiation.- Change of variable in R^d.- Differentiation of measures.- Differentiation of functions.- 7. Measures on Locally Compact Spaces.- Locally compact spaces.- The Riesz representation theorem.- Signed and complex measures; duality.- Additional properties of regular measures.- The µ^*-measurable sets and the dual of L^1.- Products of locally compact spaces.- 8. Polish Spaces and Analytic Sets.- Polish spaces.- Analytic sets.- The separation theorem and its consequences.- The measurability of analytic sets.- Cross sections.- Standard, analytic, Lusin, and Souslin spaces.- 9. Haar Measure.- Topological groups.- The existence and uniqueness of Haar measure.- The algebras L^1 (G) and M (G).- Appendices.- A. Notation and set theory.- B. Algebra.- C. Calculus and topology in R^d.- D. Topological spaces and metric spaces.- E. The Bochner integral.- F Liftings.- G The Banach-Tarski paradox.- H The Henstock-Kurzweil and McShane integralsBibliography.- Index of notation.- Index.

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Trade Review“This book is the result … of a fruitful and long collaboration between a mathematician and a cell biologist. Capturing the best of both worlds, the book provides not only the biology and mathematical background for this topic, but also offers numerous examples which render it accessible to (post-graduate) students and researchers … . this book can be treated as an excellent textbook for a wide audience varying from students to lecturers.” (Irina Ioana Mohorianu, zbMATH 1312.92004, 2015)"This book treats the theory of several important types of branching processes and demonstrates their usefulness by many interesting and important applications. … Mathematical theory and biological applications are nicely interwoven. This text will be useful both to mathematicians (including graduate students) interested in relevant applications of stochastic processes in biology, as well as to mathematically oriented biologists working on the above mentioned topics." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (1), 2004)"This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Charles J. Mode, Siam Review, Vol. 45 (2), 2003)"This is a book written jointly by a mathematician and a cell biologist, who have collaborated on research in branching processes for more than a decade. In their own words, their monograph is intended for ‘mathematicians and statisticians who have had an introduction to stochastic processes but have forgotten much of their college biology, and for biologists who wish to collaborate with mathematicians and statisticians.’ They have largely succeeded in achieving their goal. The book can be strongly recommended to all students of branching processes; all libraries should have a copy." —ZENTRALBLATT MATH Table of ContentsMotivating Examples and Other Preliminaries.- Biological Background.- The Galton-Watson Process.- The Age-Dependent Process: Markov Case.- The Bellman-Harris Process.- Multitype Processes.- Branching Processes with Infinitely Many Types.- Genealogies of Branching Processes and their Applications.- References.

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Book SynopsisAn Excel Companion for an Introductory Statistics Course in Social and Behavioral Sciences introduces students to the use of Excel to perform basic and intermediate data analyses that are common in the social and behavioral sciences. The companion focuses on using Excel to perform the types of analyses covered in most textbooks within the discipline.The book covers computations of descriptive statistics, hypothesis testing for means up to one-way ANOVA, correlation, and simple linear regression. Students learn how to perform summation in Excel, build pivot tables, and create compelling and accurate distribution graphs. Measures of central tendency, variability, and location are covered. Additional chapters explore normal distribution, random numbers, probability distributions, cross tabulations, and more.All Excel computations described in the companion rely on basic Excel functions and the Data Analysis ToolPak add-on that comes with Excel. Highly practical and accessible, An Excel Companion for an Introductory Statistics Course in Social and Behavioral Sciences is an ideal supplementary text for introductory statistics courses.

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Book SynopsisBusiness Statistics with Solutions in R covers a wide range of applications of statistics in solving business related problems. It will introduce readers to quantitative tools that are necessary for daily business needs and help them to make evidence-based decisions. The book provides an insight on how to summarize data, analyze it, and draw meaningful inferences that can be used to improve decisions. It will enable readers to develop computational skills and problem-solving competence using the open source language, R. Mustapha Abiodun Akinkunmi uses real life business data for illustrative examples while discussing the basic statistical measures, probability, regression analysis, significance testing, correlation, the Poisson distribution, process control for manufacturing, time series analysis, forecasting techniques, exponential smoothing, univariate and multivariate analysis including ANOVA and MANOVA and more in this valuable reference for policy makers, professionals, academics and individuals interested in the areas of business statistics, applied statistics, statistical computing, finance, management and econometrics.Table of ContentsChapter One: Introduction to Statistical Analysis 1.1 Scale of measurement 1.2 Data, data collection and presentation 1.3 Data grouping 1.4 Methods of visualizing data 1.5 Introduction to R software Chapter Two: Descriptive Data Chapter One: Introduction to Statistical Analysis Scale of measurement Data, data collection and presentation Data grouping Methods of visualizing data Introduction to R software Chapter Two: Descriptive Data 2.1. Measure of Central tendency 2.2. Measure of Dispersion 2.3. Shapes of the distribution—symmetric and asymmetric 2.4. Summary statistics of data using R Chapter Three: Basic Probability Concepts 3.1. Experiment and sample space 3.2. Elementary events 3.3 Venn diagram and probability matrices for two sets probability problems. 3.4 Addition rule of probability 3.5 Independent events and dependent events. 3.6 Multiplication rule of probability 3.7 Conditional probabilities 　 Chapter Four: Discrete Probability Distributions 4.1. Expected value and variance of a discrete random variable 4.2. Binomial probability distribution 4.3. Expected value and variance of a binomial distribution 4.4. Solve problems involving binomial distribution using R Chapter Five: Continuous Probability Distribution 5.1. Normal distribution and standardized normal distribution 5.2. Normal curve 5.3. Approximate normal to the binomial distribution 5.4. Use of the normal distribution in business problem solving using R Chapter Six: Sampling and Sampling Distribution 6.1. Probability and non-probability sampling 6.2. Sampling techniques- simple random, systematic, stratified, and cluster samples 6.3. Sampling distribution of the mean 6.4. Central limit theorem and its significance Chapter Seven: Confidence Intervals for Single Population Mean and Proportion 7.1. Point estimates and interval estimates 7.2. Confidence intervals for mean and proportion 7.3. Confidence interval for proportion 7.4 Factors that determine margin of error 　 Chapter Eight: Hypothesis Testing for Single Population Mean and Proportion 8.1. Null and alternative hypotheses 8.2 Type I and Type II Error 8.3. Acceptance and Rejection regions 8.4. Hypothesis testing procedure Chapter Nine: Regression Analysis and Correlation 9.1. Construction of line fit plots 9.2. Types of regression analysis 9.2.1 Uses of regression analysis 9.2.2 Simple linear regression 9.2.3 Assumptions of simple linear regression 9.3. Multiple linear regression 9.3.1 Significance testing of each variable 9.3.2. Interpretation of regression coefficients and other output 9.4 Pearson correlation coefficient 9.4.1 Assumptions of correlation test 9.4.2 Types of correlation 9.4.3 Coefficient of determination 9.4.4 Test for the significance of correlation coefficient (r) Chapter Ten: Poisson Distribution 10.1. Poisson distribution and its properties 10.2. Mean and variance of a Poisson distribution 10.3. Application of Poisson distribution 10.4. Poisson to approximate the Binomial 　 Chapter Eleven: Uniform Distribution 11.1. Uniform distribution and its properties 11.2. Mean and variance of a uniform distribution 11.3. Application of uniform distribution Chapter Twelve: Statistical Process Control 12.1. Types of control chart 12.2 Uses of control chart 12.3 Procedure of control chart 12.4. Variable control charts 12.4.1. X-bar chart 12.4.1.1. Steps for constructing X-bar chart 12.4.2. Range chart 12.4.2.1. Steps for constructing R-chart 12.4.3. S-chart 12.4.4. NP chart 12.4.5. P chart 12.4.6. C chart 12.4.7. U chart 　 Chapter Thirteen: Time Series 13.1. Concept of Time series data 13.1.1 Uses and application of time series analysis 13.2 Univariate time series model 13.2.1 Generating a time-series object in R 13.2.2. Smoothing and seasonal decomposition 13.2.2.3. Exponential Forecasting Models 13.2.2.4. Holt and Holt-Winters exponential smoothing 13.2.2.5 The ets( ) function and automated forecasting 13.2.2.5. ARIMA forecasting models 13.3 Multivariate time series model 13.3.1. ARMA and ARIMA models 13.4 Recap 　 Chapter Fourteen: Multivariate Analysis 14.1. Properties of Multivariate Normal Distribution 14.2. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation 14.2.1. Multivariate Normal Distribution 14.2.2 Maximum Likelihood Estimation of Mean (μ) and Covariance matrix (Σ) 14.3 The Sampling Distribution X ̅ and 14.3.1 Wishart Distribution 14.3.2 Properties of the Wishart Distribution 14.3.3 Large Sample Properties of X ̅ and 14.4 Multivariate Normality 14.4.1 Q-Q Plot for Evaluating Multivariate Normality 14.4.1.1 Steps for Constructing Chi-squared plot 　 　 Chapter Fifteen: Inference About a Mean Vector 15.1 Test of Hypothesis [μ=μ_0] 15.2 Confidence Interval and Simultaneous Comparison of Component Means 15.2.1 Confidence Regions 15.2.2 Simultaneous Confidence Intervals 15.2.3 Bonferroni Method of Multiple Comparisons 15.2.3 Large Sample Inference about a Population Mean Vector 15.2.4 Multivariate Quality Control Charts 15.2.4.1 Univariate Case 15.2.4.1 Multivariate Case Chapter Sixteen: Inference About a Mean Vector 16.1 Paired Comparisons 16.2 Repeated Measurement Comparisons 16.3 Comparisons of Mean Vectors from Two Populations 16.4 Several Multivariate Population Means Comparison. 16.4.1 Univariate Analysis of Variance (ANOVA) 16.4.1.1 Assumptions of ANOVA 16.4.2 Multivariate Analysis of Variance (MANOVA) 16.4.2.1 Assumptions of MANOVA

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Book SynopsisThis business analytics (BA) text discusses the models based on fact-based data to measure past business performance to guide an organization in visualizing and predicting future business performance and outcomes.It provides a comprehensive overview of analytics in general with an emphasis on predictive analytics. Given the booming interest in analytics and data science, this book is timely and informative. It brings many terms, tools, and methods of analytics together.The first three chapters provide an introduction to BA, importance of analytics, types of BA—descriptive, predictive, and prescriptive—along with the tools and models. Business intelligence (BI) and a case on descriptive analytics are discussed. Additionally, the book discusses on the most widely used predictive models, including regression analysis, forecasting, data mining, and an introduction to recent applications of predictive analytics—machine learning, neural networks, and artificial intelligence. The concluding chapter discusses on the current state, job outlook, and certifications in analytics.

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Book SynopsisThis book is a convenient and comprehensive guide to statistics. A resource for quality technicians and engineers in any industry, this second edition provides even more equations and examples for the reader-with a continued focus on algebra-based math. Those preparing for ASQ certification examinations, such as the Certified Quality Technician (CQT), Certified Six Sigma Green Belt (CSSGB), Certified Quality Engineer (CQE), Certified Six Sigma Black Belt (CSSBB), Certified Reliability Engineer (CRE), and Certified Supplier Quality Professional (CSQP), will find this book helpful as well. Inside you''ll find: Complete calculations for determining confidence intervals, tolerances, sample size, outliers, process capability, and system reliability Newly added equations for hypothesis tests (such as the Kruskal-Wallis test and Levene''s test for equality of variances), the Taguchi method, and Weibull and log-normal distributions Hundreds of completed examples to demonstrate practical use of each equation 20+ appendices, including distribution tables, critical values tables, control charts, sampling plans, and a beta table

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