Probability and Statistical Inference

by ;
Edition: 2nd
Format: Hardcover
Pub. Date: 2008-01-02
Publisher(s): Wiley-Interscience
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Summary

Now updated in a valuable new edition, this book introduces key probability and statistical concepts through non-trivial, real-world examples and promotes the development of intuition rather than simple application. With its coverage of the recent advancements in computer-intensive methods, this update successfully provides the comprehensive tools needed to develop a broad understanding of the theory of statistics and its probabilistic foundations.

Author Biography

The late Robert Bartoszynski, PhD, was Professor in the Department of Statistics at The Ohio State University. His scientific contributions included research in the theory of stochastic processes and modeling biological phenomena. Throughout his career, Dr. Bartoszynski published over 80 journal articles, books, and book chapters. He was a Fellow of the Institute of Mathematical Statistics as well as a member of the American Statistical Association, the International Statistical Institute, and the Bernoulli Society.

Magdalena Niewiadomska-Bugaj, PhD, is Professor in the Department of Statistics at Western Michigan University. An active member of numerous societies including the American Statistical Association, the Institute of Mathematical Statistics, and the Classification Society of North America, Dr. Niewiadomska-Bugaj's areas of interest include general statistical methodology, nonparametric statistics, classification, and categorical data analysis. She has published over 50 papers, books, and book chapters in theoretical and applied statistics.

Table of Contents

Prefacep. x
Experiments, Sample Spaces, and Eventsp. 1
Introductionp. 1
Sample Spacep. 2
Algebra of Eventsp. 9
Infinite Operations on Eventsp. 16
Probabilityp. 25
Introductionp. 25
Probability as a Frequencyp. 25
Axioms of Probabilityp. 26
Consequences of the Axiomsp. 31
Classical Probabilityp. 36
Necessity of the Axiomsp. 37
Subjective Probabilityp. 42
Countingp. 47
Introductionp. 47
Product Sets, Orderings, and Permutationsp. 47
Binomial Coefficientsp. 55
Extension of Newton's Formulap. 68
Multinomial Coefficientsp. 69
Conditional Probability: Independencep. 73
Introductionp. 73
Conditional Probabilityp. 74
Partitions; Total Probability Formulap. 80
Bayes' Formulap. 87
Independencep. 92
Exchangeability; Conditional Independencep. 99
Markov Chains*p. 103
Introduction and Basic Definitionsp. 103
Definition of a Markov Chainp. 106
n-Step Transition Probabilitiesp. 111
The Ergodic Theoremp. 114
Absorption Probabilitiesp. 122
Random Variables: Univariate Casep. 125
Introductionp. 125
Distributions of Random Variablesp. 126
Discrete and Continuous Random Variablesp. 139
Functions of Random Variablesp. 150
Survival and Hazard Functionsp. 157
Random Variables: Multivariate Casep. 161
Bivariate Distributionsp. 161
Marginal Distributions; Independencep. 168
Conditional Distributionsp. 180
Bivariate Transformationsp. 187
Multidimensional Distributionsp. 196
Expectationp. 203
Introductionp. 203
Expected Valuep. 204
Expectation as an Integral*p. 212
Properties of Expectationp. 220
Momentsp. 228
Variancep. 236
Conditional Expectationp. 248
Inequalitiesp. 252
Selected Families of Distributionsp. 257
Bernoulli Trials and Related Distributionsp. 257
Hypergeometric Distributionp. 270
Poisson Distribution and Poisson Processp. 276
Exponential, Gamma and Related Distributionsp. 290
Normal Distributionp. 296
Beta Distributionp. 306
Random Samplesp. 311
Statistics and their Distributionsp. 311
Distributions Related to Normalp. 313
Order Statisticsp. 319
Generating Random Samplesp. 325
Convergencep. 330
Central Limit Theoremp. 342
Introduction to Statistical Inferencep. 351
Overviewp. 351
Descriptive Statisticsp. 353
Basic Modelp. 358
Bayesian Statisticsp. 360
Samplingp. 360
Measurement Scalesp. 367
Estimationp. 373
Introductionp. 373
Consistencyp. 378
Loss, Risk, and Admissibilityp. 381
Efficiencyp. 386
Methods of Obtaining Estimatorsp. 394
Sufficiencyp. 424
Interval Estimationp. 440
Testing Statistical Hypothesesp. 455
Introductionp. 455
Intuitive Backgroundp. 460
Most Powerful Testsp. 469
Uniformly Most Powerful Testsp. 481
Unbiased Testsp. 487
Generalized Likelihood Ratio Testsp. 491
Conditional Testsp. 498
Tests and Confidence Intervalsp. 501
Review of Tests for Normal Distributionsp. 502
Monte Carlo, Bootstrap, and Permutation Testsp. 512
Linear Modelsp. 517
Introductionp. 517
Regression of the First and Second Kindp. 519
Distributional Assumptionsp. 525
Linear Regression in the Normal Casep. 528
Testing Linearityp. 535
Predictionp. 538
Inverse Regressionp. 540
BLUEp. 542
Regression Toward the Meanp. 545
Analysis of Variancep. 546
One-Way Layoutp. 547
Two-Way Layoutp. 550
ANOVA Models with Interactionp. 553
Further Extensionsp. 557
Rank Methodsp. 559
Introductionp. 559
Glivenko-Cantelli Theoremp. 560
Kolmogorov-Smirnov Testsp. 564
One-Sample Rank Testsp. 571
Two-Sample Rank Testsp. 578
Kruskal-Wallis Testp. 582
Analysis of Categorical Datap. 585
Introductionp. 585
Chi-Square Testsp. 587
Homogeneity and Independencep. 593
Consistency and Powerp. 599
2 x 2 Contingency Tablesp. 604
r x c Contingency Tablesp. 612
Statistical Tablesp. 617
Bibliographyp. 629
Answers to Odd-Numbered Problemsp. 634
Indexp. 642
Table of Contents provided by Ingram. All Rights Reserved.

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