Statistical Inference: (Dover Books on Mathematics)

Unified treatment of probability and statistics examines and analyses the relationship between the two fields, exploring inferential issues. Numerous problems, examples, and diagrams--some with solutions--plus clear-cut, highlighted summaries of results. Advanced undergraduate to graduate level. Contents: 1. Introduction. 2. Probability Model. 3. Probability Distributions. 4. Introduction to Statistical Inference. 5. More on Mathematical Expectation. 6. Some Discrete Models. 7. Some Continuous Models. 8. Functions of Random Variables and Random Vectors. 9. Large-Sample Theory. 10. General Methods of Point and Interval Estimation. 11. Testing Hypotheses. 12. Analysis of Categorical Data. 13. Analysis of Variance: k-Sample Problems. Appendix-Tables. Answers to Odd-Numbered Problems. Index. Unabridged republication of the edition published by John Wiley & Sons, New York, 1984. 144 Figures. 35 Tables. Errata list prepared by the author

Table of Contents:
CHAPTER 1. INTRODUCTION 1.1 Introduction 1.2 Stochastic Models 1.3 "Probability, Statistics, and Inference" CHAPTER 2. PROBABILITY MODEL 2.1 Introduction 2.2 Sample Space and Events 2.3 Probability Axioms 2.4 Elementary Consequences of Axioms 2.5 Counting Methods 2.6 Conditional Probability 2.7 Independence 2.8 Simple Random Sampling from a Finite Population 2.9 Review Problems CHAPTER 3 PROBABILITY DISTRIBUTIONS 3.1 Introduction 3.2 Random Variables and Random Vectors 3.3 Describing a Random Variable 3.4 Multivariate Distributions 3.5 Marginal and Conditional Distributions 3.6 Independent Random Variables 3.7 Numerical Characteristics of a Distribution- Expected Value 3.8 Random Sampling from a Probability Distribution 3.9 Review Problems CHAPTER 4 INTRODUCTION TO STATISTICAL INFERENCE 4.1 Introduction 4.2 Parametric and Nonparametric Families 4.3 Point and Interval Estimatimation 4.4. Testing Hypotheses 4.5 Fitting the Underlying Distribution 4.6 Review Problems CHAPTER 5. MORE ON MATHEMATICAL EXPECTATION 5.1 Introduction 5.2 Moments in the Multivariate Case 5.3 Linear Combintions of Random Variables 5.4 The Law of Large Numbers 5.5* Conditional Expectation 5.6 Review Problems CHAPTER 6. SOME DISCRETE MODELS 6.1 Introduction 6.2 Discrete Uniform Distribution 6.3 Bernoulli and Binomial Distributions 6.4 Hypergeometric Distribution 6.5 Geometric and Negative Binomial Distributions: Discrete Waiting-Time Distribution 6.6 Poisson Distribution 6.7 Multivariate Hypergeometric and Multinomial Distributions 6.8 Review Problems CHAPTER 7. SOME CONTINUOUS MODELS 7.1 Introduction 7.2 Uniform Distribution 7.3 Gamma and Beta Functions 7.4 "Exponential,Gamma, and Weibull Distributions" 7.5* Beta Distribution 7.6 Normal Distribution 7.7* Bivariate Normal Distribution 7.8 Review Problems CHAPTER 8. FUNCTIONS OF RANDOM VARIABLES AND RANDOM VECTORS 8.1 Introduction 8.2 The Method of Distribution Functions 8.3* The Method of Transformations 8.4 "Distributions of Sum, Product, and Quotient of Two Random Variables" 8.5 Order Statistics 8.6* Generating Functions 8.7 Sampling From a Normal Population 8.8 Review Problems CHAPTER 9. LARGE-SAMPLE THEORY 9.1 Introduction 9.2 Approximating Distributions: Limiting Moment Generating Function 9.3 The Central Limit Theorem of Levy 9.4 "The Normal Approximation to Binomial, Poisson, and Other Integer-Valued Random Variables" 9.5 Consistency 9.6 Large-Sample Point and Interval Estimation 9.7 Large-Sample Hypothesis Testing 9.8 Inference Concerning Quantiles 9.9 Goodness of Fit for Multinomial Distribution: Prespecified Cell Probabilities 9.10 Review Problems CHAPTER 10. GENERAL METHODS OF POINT AND INTERVAL ESTIMATION 10.1 Introduction 10.2 Sufficiency 10.3 Unbiased Estimation 10.4 The Substitution Principle (The Method of Moments) 10.5 Maximum Likelihood Estimation 10.6* Bayesian Estimation 10.7 Confidence Intervals 10.8 Review Problems CHAPTER 11 TESTING HYPOTHESES 11.1 Introduction 11.2 Neyman-Pearson Lemma 11.3* Composite Hypotheses 11.4* Likelihood Ratio Tests 11.5 The Wilcoxon Signed Rank Test 11.6 Some Two-Sample Tests 11.7 Chi-Square Test of Goodness of Fit Revisited 11.8* Kolmogorov-Smirnov Goodness of Fit Test 11.9 Measures of Association for Bivariate Data 11.10 Review Problems CHAPTER 12. ANALYSIS OF CATEGORICAL DATA 12.1 Introduction 12.2 Chi-Square Test for Homogeneity 12.3 Testing Independence in Contingency Tables 12.4 Review Problems CHAPTER 13 ANALYSIS OF VARIANCE: k-SAMPLE PROBLEMS 13.1 Introduction 13.2 One-Way Analysis of Variance 13.3 Multiple Comparisonof Means 13.4 Two-Way Analysis of Variance 13.5 Testing Equality in k-Independent Samples: Nonnormal Case 13.6 The Friedman Test for k-Related Samples 13.7 Review Problems APPENDIX-TABLES ANSWERS TO ODD-NUMBERED PROBLEMS INDEX ERRATA