Introduction to Mathematical Statistics, Global Edition, 8th Edition
- Length: 762 pages
- Edition: 8
- Language: English
- Publisher: Pearson
- Publication Date: 2020-01-13
- ISBN-10: 1292264764
- ISBN-13: 9781292264769
- Sales Rank: #1482659 (See Top 100 Books)
For courses in mathematical statistics.
Comprehensive coverage of mathematical statistics – with a proven approach
Introduction to Mathematical Statistics by Hogg, McKean, and Craig enhances student comprehension and retention with numerous, illustrative examples and exercises. Classical statistical inference procedures in estimation and testing are explored extensively, and the text’s flexible organization makes it ideal for a range of mathematical statistics courses.
Substantial changes to the 8th Edition – many based on user feedback – help students appreciate the connection between statistical theory and statistical practice, while other changes enhance the development and discussion of the statistical theory presented.
Front Cover Title Page Copyright Page Dedication Page Contents Preface 1 Probability and Distributions 1.1 Introduction 1.2 Sets 1.2.1 Review of Set Theory 1.2.2 Set Functions 1.3 The Probability Set Function 1.3.1 Counting Rules 1.3.2 Additional Properties of Probability 1.4 Conditional Probability and Independence 1.4.1 Independence 1.4.2 Simulations 1.5 Random Variables 1.6 Discrete Random Variables 1.6.1 Transformations 1.7 Continuous Random Variables 1.7.1 Quantiles 1.7.2 Transformations 1.7.3 Mixtures of Discrete and Continuous Type Distributions 1.8 Expectation of a Random Variable 1.8.1 R Computation for an Estimation of the Expected Gain 1.9 Some Special Expectations 1.10 Important Inequalities 2 Multivariate Distributions 2.1 Distributions of Two Random Variables 2.1.1 Marginal Distributions 2.1.2 Expectation 2.2 Transformations: Bivariate Random Variables 2.3 Conditional Distributions and Expectations 2.4 Independent Random Variables 2.5 The Correlation Coefficient 2.6 Extension to Several Random Variables 2.6.1 *Multivariate Variance-Covariance Matrix 2.7 Transformations for Several Random Variables 2.8 Linear Combinations of Random Variables 3 Some Special Distributions 3.1 The Binomial and Related Distributions 3.1.1 Negative Binomial and Geometric Distributions 3.1.2 Multinomial Distribution 3.1.3 Hypergeometric Distribution 3.2 The Poisson Distribution 3.3 The Γ, χ2, and β Distributions 3.3.1 The χ2-Distribution 3.3.2 The β-Distribution 3.4 The Normal Distribution 3.4.1 *Contaminated Normals 3.5 The Multivariate Normal Distribution 3.5.1 Bivariate Normal Distribution 3.5.2 *Multivariate Normal Distribution, General Case 3.5.3 *Applications t- and F-Distributions 3.6.1 The t-distribution 3.6.2 The F-distribution 3.6.3 Student’s Theorem 3.7 *Mixture Distributions 4 Some Elementary Statistical Inferences 4.1 Sampling and Statistics 4.1.1 Point Estimators 4.1.2 Histogram Estimates of Pmfs and Pdfs 4.2 Confidence Intervals 4.2.1 Confidence Intervals for Difference in Means 4.2.2 Confidence Interval for Difference in Proportions 4.3 *Confidence Intervals for Parameters of Discrete Distributions 4.4 Order Statistics 4.4.1 Quantiles 4.4.2 Confidence Intervals for Quantiles 4.5 Introduction to Hypothesis Testing 4.6 Additional Comments About Statistical Tests 4.6.1 Observed Significance Level, p-value 4.7 Chi-Square Tests 4.8 The Method of Monte Carlo 4.8.1 Accept–Reject Generation Algorithm 4.9 Bootstrap Procedures 4.9.1 Percentile Bootstrap Confidence Intervals 4.9.2 Bootstrap Testing Procedures 4.10 *Tolerance Limits for Distributions 5 Consistency and Limiting Distributions 5.1 Convergence in Probability 5.1.1 Sampling and Statistics 5.2 Convergence in Distribution 5.2.1 Bounded in Probability 5.2.2 Δ-Method 5.2.3 Moment Generating Function Technique 5.3 Central Limit Theorem 5.4 *Extensions to Multivariate Distributions 6 Maximum Likelihood Methods 6.1 Maximum Likelihood Estimation 6.2 Rao–Cram´er Lower Bound and Efficiency 6.3 Maximum Likelihood Tests 6.4 Multiparameter Case: Estimation 6.5 Multiparameter Case: Testing 6.6 The EM Algorithm 7 Sufficiency 7.1 Measures of Quality of Estimators 7.2 A Sufficient Statistic for a Parameter 7.3 Properties of a Sufficient Statistic 7.4 Completeness and Uniqueness 7.5 The Exponential Class of Distributions 7.6 Functions of a Parameter 7.6.1 Bootstrap Standard Errors 7.7 The Case of Several Parameters 7.8 Minimal Sufficiency and Ancillary Statistics 7.9 Sufficiency, Completeness, and Independence 8 Optimal Tests of Hypotheses 8.1 Most Powerful Tests 8.2 Uniformly Most Powerful Tests 8.3 Likelihood Ratio Tests 8.3.1 Likelihood Ratio Tests for Testing Means of Normal Distributions 8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions 8.4 *The Sequential Probability Ratio Test 8.5 *Minimax and Classification Procedures 8.5.1 Minimax Procedures 8.5.2 Classification 9 Inferences About Normal Linear Models 9.1 Introduction 9.2 One-Way ANOVA 9.3 Noncentral χ2 and F-Distributions 9.4 Multiple Comparisons 9.5 Two-Way ANOVA 9.5.1 Interaction Between Factors 9.6 A Regression Problem 9.6.1 Maximum Likelihood Estimates 9.6.2 *Geometry of the Least Squares Fit 9.7 A Test of Independence 9.8 The Distributions of Certain Quadratic Forms 9.9 The Independence of Certain Quadratic Forms 10 Nonparametric and Robust Statistics 10.1 Location Models 10.2 Sample Median and the Sign Test 10.2.1 Asymptotic Relative Efficiency 10.2.2 Estimating Equations Based on the Sign Test 10.2.3 Confidence Interval for the Median 10.3 Signed-Rank Wilcoxon 10.3.1 Asymptotic Relative Efficiency 10.3.2 Estimating Equations Based on Signed-Rank Wilcoxon 10.3.3 Confidence Interval for the Median 10.3.4 Monte Carlo Investigation 10.4 Mann–Whitney–Wilcoxon Procedure 10.4.1 Asymptotic Relative Efficiency 10.4.2 Estimating Equations Based on the Mann–Whitney– Wilcoxon 10.4.3 Confidence Interval for the Shift Parameter Δ 10.4.4 Monte Carlo Investigation of Power 10.5 *General Rank Scores 10.5.1 Efficacy 10.5.2 Estimating Equations Based on General Scores 10.5.3 Optimization: Best Estimates 10.6 *Adaptive Procedures 10.7 Simple Linear Model 10.8 Measures of Association 10.8.1 Kendall’s τ 10.8.2 Spearman’s Rho 10.9 Robust Concepts 10.9.1 Location Model 10.9.2 Linear Model 11 Bayesian Statistics 11.1 Bayesian Procedures 11.1.1 Prior and Posterior Distributions 11.1.2 Bayesian Point Estimation 11.1.3 Bayesian Interval Estimation 11.1.4 Bayesian Testing Procedures 11.1.5 Bayesian Sequential Procedures 11.2 More Bayesian Terminology and Ideas 11.3 Gibbs Sampler 11.4 Modern Bayesian Methods 11.4.1 Empirical Bayes A Mathematical Comments A.1 Regularity Conditions A.2 Sequences B R Primer B.1 Basics B.2 Probability Distributions B.3 R Functions B.4 Loops B.5 Input and Output B.6 Packages C Lists of Common Distributions D Tables of Distributions E References F Answers to Selected Exercises Index Back Cover
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