Models for Probability and Statistical Inference Theory and Applications

by Stapleton, James H.

• ISBN13: 9780470073728
• ISBN10: 0470073721
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-12-17
• Publisher: Wiley-Interscience

Summary

This textbook is an introduction to probability and statistical inference for students. It contains a large amount of figures, with simulations and graphs, produced by the statistical package S-Plus(r), included throughout. It discusses methods for the computer simulation of observations from specified distributions and provides flexibility for instructors. Each section is followed by a range of problems, from simple to more complex with selected answers.

Author Biography

James H. Stapleton, PhD, has recently retired after forty-nine years as professor in the Department of Statistics and Probability at Michigan State University, including eight years as chairperson and almost twenty years as graduate director. Dr. Stapleton is the author of Linear Statistical Models (Wiley), and he received his PhD in mathematical statistics from Purdue University.

Table of Contents

Preface	p. xi
Discrete Probability Models	p. 1
Introduction	p. 1
Sample Spaces, Events, and Probability Measures	p. 2
Conditional Probability and Independence	p. 15
Random Variables	p. 27
Expectation	p. 37
The Variance	p. 47
Covariance and Correlation	p. 55
Special Discrete Distributions	p. 62
Introduction	p. 62
The Binomial Distribution	p. 62
The Hypergeometric Distribution	p. 65
The Geometric and Negative Binomial Distributions	p. 68
The Poisson Distribution	p. 72
Continuous Random Variables	p. 80
Introduction	p. 80
Continuous Random Variables	p. 80
Expected Values and Variances for Continuous Random Variables	p. 88
Transformations of Random Variables	p. 93
Joint Densities	p. 97
Distributions of Functions of Continuous Random Variables	p. 104
Special Continuous Distributions	p. 110
Introduction	p. 110
The Normal Distribution	p. 111
The Gamma Distribution	p. 117
Conditional Distributions	p. 125
Introduction	p. 125
Conditional Expectations for Discrete Random Variables	p. 130
Conditional Densities and Expectations for Continuous Random Variables	p. 136
Moment Generating Functions and Limit Theory	p. 145
Introduction	p. 145
Moment Generating Functions	p. 145
Convergence in Probability and in Distribution and the Weak Law of Large Numbers	p. 148
The Central Limit Theorem	p. 155
Estimation	p. 166
Introduction	p. 166
Point Estimation	p. 167
The Method of Moments	p. 171
Maximum Likelihood	p. 175
Consistency	p. 182
The [delta]-Method	p. 186
Confidence Intervals	p. 191
Fisher Information, Cramer-Rao Bound and Asymptotic Normality of MLEs	p. 201
Sufficiency	p. 207
Testing of Hypotheses	p. 215
Introduction	p. 215
The Neyman-Pearson Lemma	p. 222
The Likelihood Ratio Test	p. 228
The p-Value and the Relationship between Tests of Hypotheses and Confidence Intervals	p. 233
The Multivariate Normal, Chi-Square, t, and F Distributions	p. 238
Introduction	p. 238
The Multivariate Normal Distribution	p. 238
The Central and Noncentral Chi-Square Distributions	p. 241
Student's t-Distribution	p. 245
The F-Distribution	p. 254
Nonparametric Statistics	p. 260
Introduction	p. 260
The Wilcoxon Test and Estimator	p. 262
One-Sample Methods	p. 271
The Kolmogorov-Smirnov Tests	p. 277
Linear Statistical Models	p. 281
Introduction	p. 281
The Principle of Least Squares	p. 281
Linear Models	p. 290
F-Tests for H[subscript 0]: [theta] = [Beta subscript 1] X[subscript 1] + ... + [Beta subscript k] X[subscript k][Epsilon] V[subscript 0], a Subspace of V	p. 299
Two-Way Analysis of Variance	p. 308
Frequency Data	p. 319
Introduction	p. 319
Confidence Intervals on Binomial and Poisson Parameters	p. 319
Logistic Regression	p. 324
Two-Way Frequency Tables	p. 330
Chi-Square Goodness-of-Fit Tests	p. 340
Miscellaneous Topics	p. 350
Introduction	p. 350
Survival Analysis	p. 350
Bootstrapping	p. 355
Bayesian Statistics	p. 362
Sampling	p. 369
References	p. 378
Appendix	p. 381
Answers to Selected Problems	p. 411
Index	p. 437
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