Transcription
Mathematical Statisticsand Data AnalysisJOHN A. RICEUniversity of California, San DiegowЙWadsworth & Brooks/Cole Advanced Books & SoftwarePacific Grove, California
CONTENTS1Probability1.11.21.31.41Introduction 1Sample Spaces 2Probability Measures 5Computing Probabilities: Counting Methods1.4.1 The Multiplication Principle 71.4.2 Permutations and Combinations 91.51.61.71.8Conditional Probability 14Independence 20Concluding Remarks 22Problems 23
XIVCONTENTS2Random Variables2.1Discrete Random Variables2.1.12.1.22.1.32.1.42.1.52.231Bernoulli Random Variables 34The Binomial Distribution 34The Geometric and Negative Binomial DistributionsThe Hypergeometric Distribution 38The Poisson Distribution 39Continuous Random Variables2.2.12.2.22.2.32.32.42.5313644The Exponential Density 46The Gamma Density 49The Normal Distribution 51Functions of a Random VariableConcluding Remarks 59Problems 59543Joint Distributions3.13.23.33.43.5Introduction 65Discrete Random Variables 67Continuous Random Variables 69Independent Random Variables 77Conditional Distributions 793.5.13.5.23.6The Discrete Case 79The Continuous Case 81Functions of Jointly Distributed Random Variables3.6.13.6.23.73.86586Sums and Quotients 86The General Case 90Extrema and Order StatisticsProblems 97944Expected Values4.1104The Expected Value of a Random Variable4.1.14.1.2104Expectations of Functions of Random Variables 109Expectations of Linear Combinations of Random Variables
CONTENTS4.2 Variance and Standard Deviation4.2.1A Model for Measurement Error1161194.3 Co variance and Correlation 1224.4 Conditional Expectation and Prediction4.4.14.4.2Definitions and ExamplesPrediction 1331281284.5 The Moment-Generating Function4.6 Approximate Methods 1424.7 Problems 1471355Limit Theorems1555.1 Introduction 1555.2 The Law of Large Numbers 1555.3 Convergence in Distribution and the Central LimitTheorem 1595.4 Problems 1666Distributions Derived from the Normal Distribution6.16.26.36.4168Introduction 168i2, t, and F Distributions 168The Sample Mean and the Sample Variance 170Problems 1747Survey Sampling1757.1 Introduction 1757.2 Population Parameters 1767.3 Simple Random Sampling 1787.3.17.3.27.3.3The Expectation and Variance of the Sample Mean 179Estimation of the Population Variance 185TheJSTormal Approximation to the Sampling Distributiono f * 1887.4 Estimation of a Ratio 1937.5 Stratified Random Sampling 201XV
XVICONTENTS7.5.17.5.27.5.37.67.7Introduction and Notation 201Properties of Stratified EstimatesMethods of Allocation 206Concluding RemarksProblems 2132022118Estimation of Parameters and Fitting of ProbabilityDistributions 2228.18.28.38.48.5Introduction 222Fitting the Poisson Distribution to Emissions of AlphaParticles 223Parameter Estimation 226The Method of Moments 230The Method of Maximum Likelihood 2348.5.18.5.28.5.38.6Efficiency and the Cramer-Rao Lower Bound8.6.18.7An Example: The Negative Binomial DistributionSufficiency8.7.18.7.28.88.9Maximum Likelihood Estimates of Multinomial CellProbabilities 238Large Sample Theory for Maximum Likelihood Estimates 241Confidence Intervals for Maximum Likelihood Estimates 245250254257A Factorization Theorem 258The Rao-Blackwell Theorem 261Concluding RemarksProblems 2632629Testing Hypotheses and Assessing Goodness of Fit 2709.19.29.39.49.59.6Introduction 270The Neyman-Pearson Paradigm 271Optimal Tests: The Neyman-Pearson Lemma 274The Duality of Confidence Intervals and HypothesisTests 276Generalized Likelihood Ratio Tests 278Likelihood Ratio Tests for the MultinomialDistribution 281
CONTENTS9.79.89.99.109.119.12The Poisson Dispersion TestHanging Rootograms 289Probability Plots 292Tests for Normality 299Concluding Remarks 301Problems 30210Summarizing DataXVII28631210.1 Introduction 31210.2 Methods Based on the Cumulative DistributionFunction 31310.2.1 The Empirical Cumulative Distribution Function10.2.2 The Survival Function 31510.2.3 Quantile-Quantile Plots 32010.310.4Histograms, Density Curves, and Stem-and-LeafPlots 324Measures of Location 13The Arithmetic Mean 328The Median 331The Trimmed Mean 332M Estimates 333Comparison of Location Estimates334Measures of Dispersion 335Boxplots 336Concluding Remarks 338Problems 33811Comparing Two Samples34711.1 Introduction 34711.2 Comparing Two Independent Samples11.2.1348Methods Based on the Normal Distribution 34811.2.1.1 An Example—A Study of Iron Retention 35611.2.2 Power 36111.2.3 A Nonparametric Method—The Mann-Whitney Test 36411.3 Comparing Paired Samples371
XV111CONTENTS11.3.1 Methods Based on the Normal Distribution 37211.3.2 A Nonparametric Method—The Signed Rank Test 37411.3.3 An Example—Measuring Mercury Levels in Fish 37611.4Experimental .4.811.5 Concluding Remarks11.6 Problems 38512378Mammary Artery Ligation 378The Placebo Effect 378The Lanarkshire Milk Experiment 379The Portocaval Shunt 380F D & C R e d N o . 40 380Further Remarks on Randomization 382Observational Studies, Confounding, and Bias in GraduateAdmissions 382Fishing Expeditions 383The Analysis of Variance38439612.1 Introduction 39612.2 The One-Way Layout39612.2.1 Normal Theory; the F Test 39812.2.2 The Problem of Multiple Comparisons 40412.2.2.1 Tukey's Method 40412.2.2.2 The Bonferroni Method 40612.2.3 A Nonparametric Method—The Kruskal-Wallis Test12.3 The Two-Way Layout40812.3.1 Additive Parametrization 40812.3.2 Normal Theory for the Two-Way Layout 41112.3.3 Randomized Block Designs 41912.3.4 A Nonparametric Method—Friedman's Test 42212.4 Concluding Remarks12.5 Problems 42513424The Analysis of Categorical Data13.113.213.313.4434Introduction 434Fisher's Exact Test 434The Chi-Square Test of HomogeneityThe Chi-Square Test of Independence436441406
CONTENTS13.5 Matched-Pairs Designs 44313.6 Concluding Remarks 44613.7 Problems 44714Linear Least Squares45314.1 Introduction 45314.2 Simple Linear Regression45914.2.1Statistical Properties of the Estimated Slope andIntercept 45914.2.2 Assessing the Fit 46214.2.3 Correlation and Regression 47214.3 The Matrix Approach to Linear Least Squares 47414.4 Statistical Properties of Least Squares Estimates 47814.4.1 Vector-Valued Random Variables 47814.4.2 Mean and Covariance of Least Squares Estimates14.4.3 Estimation of a2 48514.4.4 Residuals and Standardized Residuals 48714.4.5 Inference about ß 48814.5 Multiple Linear Regression—An Example14.6 Concluding Remarks 49514.7 Problems 49648349115Decision Theory and Bayesian Inference51115.1 Introduction 51115.2 Decision Theory 51115.2.1 Bayes Rules and Minimax Rules 51315.2.2 Posterior Analysis 51815.2.3 Classification and Hypothesis Testing 52215.2.4 Estimation 52515.3 The Subjectivist Point of View15.3.115.3.2529Bayesian Inference for the Normal Distribution 530Bayesian Analysis for the Binomial Distribution 53415.4 Concluding Remarks15.5 Problems 539539xix
XXCONTENTSBibliography 545Appendix A Common DistributionsAppendix В Tables 555Answers to Selected Problems 575Index to Data Sets 585Author Index 587Subject Index 589551
Mathematical Statistics and Data Analysis JOHN A. RICE University of California, San Diego w Й Wadsworth & Brooks/Cole Advanced Books & Software Pacific Grove, California . CONTENTS 1 Probability 1 1.1 Introduction 1 1.2 Sample Spaces 2 1.3 Probability Measures 5 1.4 Computing Probabilities: Counting Methods 1.4.1 The Multiplication Principle 7 1.4.2 Permutations and
