概率統計

概率統計

作者:（美）Morris H．DeGroot/（美）Mark J．Schervish

出版社:機械工業出版社

副標題：概率統計

原作名:Probability and Statistics(Fourth Edition)

出版年:2012-7

頁數:904

定價:139.00元

叢書：華章統計學原版精品系列

ISBN:9787111387756

這本經典的概率論與數理統計教材，多年來暢銷不衰，被很多名校採用，包括卡內基梅隆大學、哈佛大學、麻省理工學院、華盛頓大學、芝加哥大學、康乃爾大學、杜克大學、加州大學洛杉磯分校等。

本書包括概率論、數理統計兩部分，內容豐富完整，適當地選擇某些章節，可以作為一學年的概率論與數理統計課程的教材，亦可作為一學期的概率論與隨機過程的教材。適合數學、統計學、經濟學等專業高年級本科生和研究生用，也可供統計工作人員用作參考書。

本書主要特點

 敘述清晰易懂，內容深入淺出。作者用大量頗具啟發性的例子引入論題、闡釋理論和證明。例題涉及面廣，除了那些解釋基本概念的一些著名例題外，還有很多新穎的例題，描述了概率論在遺傳學、排隊論、計算金融學和計算機科學中的應用。

Morris H. DeGroot(1931–1989) 世界著名的統計學家。生前曾任國際統計學會、美國科學促進會、統計學會、數理統計學會、計量經濟學會會士。卡內基梅隆大學教授，1957年加入該校，1966年創辦該校統計系。DeGroot在學術上異常活躍和多產，曾發表一百多篇論文，還著有 Optimal Statistical Decisions和 Statistics and the Law。為紀念他的著作對統計教學的貢獻，國際貝葉斯分析學會特別設立了DeGroot獎表彰優秀統計學著作。

Mark J. Schervish 世界著名的統計學家，美國統計學會、數理統計學會會士。於1979年獲得伊利諾大學的博士學位，之後就在卡內基梅隆大學統計系工作，教授數學、概率、統計和計算金融等課程，現為該系系主任。Schervish在學術上非常活躍，成果頗豐，還因在統計推斷和貝葉斯統計方面的基石性工作而聞名，除本書外，他還著有Theory of Statistics和 Rethinking the Foundations of Statistics。

Contents

1 Introduction to Probability 1

1.1 The History of Probability 1

1.2 Interpretations of Probability 2

1.3 Experiments and Events 5

1.4 Set Theory 6

1.5 The Definition of Probability 16

1.6 Finite Sample Spaces 22

1.7 Counting Methods 25

1.8 Combinatorial Methods 32

1.9 Multinomial Coefficients 42

1.10 The Probability of a Union of Events 46

1.11 Statistical Swindles 51

1.12 Supplementary Exercises 53

2 Conditional Probability 55

2.1 The Definition of Conditional Probability 55

2.2 Independent Events 66

2.3 Bayes’ Theorem 76

2.4 The Gambler’s Ruin Problem 86

2.5 Supplementary Exercises 90

3 Random Variables and Distributions 93

3.1 Random Variables and Discrete Distributions 93

3.2 Continuous Distributions 100

3.3 The Cumulative Distribution Function 107

3.4 Bivariate Distributions 118

3.5 Marginal Distributions 130

3.6 Conditional Distributions 141

3.7 Multivariate Distributions 152

3.8 Functions of a Random Variable 167

3.9 Functions of Two or More Random Variables 175

3.10 Markov Chains 188

3.11 Supplementary Exercises 202

4 Expectation 207

4.1 The Expectation of a Random Variable 207

4.2 Properties of Expectations 217

4.3 Variance 225

4.4 Moments 234

4.5 The Mean and the Median 241

4.6 Covariance and Correlation 248

4.7 Conditional Expectation 256

4.8 Utility 265

4.9 Supplementary Exercises 272

5 Special Distributions 275

5.1 Introduction 275

5.2 The Bernoulli and Binomial Distributions 275

5.3 The Hypergeometric Distributions 281

5.4 The Poisson Distributions 287

5.5 The Negative Binomial Distributions 297

5.6 The Normal Distributions 302

5.7 The Gamma Distributions 316

5.8 The Beta Distributions 327

5.9 The Multinomial Distributions 333

5.10 The Bivariate Normal Distributions 337

5.11 Supplementary Exercises 345

6 Large Random Samples 347

6.1 Introduction 347

6.2 The Law of Large Numbers 348

6.3 The Central Limit Theorem 360

6.4 The Correction for Continuity 371

6.5 Supplementary Exercises 375

7 Estimation 376

7.1 Statistical Inference 376

7.2 Prior and Posterior Distributions 385

7.3 Conjugate Prior Distributions 394

7.4 Bayes Estimators 408

7.5 Maximum Likelihood Estimators 417

7.6 Properties of Maximum Likelihood Estimators 426

7.7 Sufficient Statistics 443

7.8 Jointly Sufficient Statistics 449

7.9 Improving an Estimator 455

7.10 Supplementary Exercises 461

8 Sampling Distributions of Estimators 464

8.1 The Sampling Distribution of a Statistic 464

8.2 The Chi-Square Distributions 469

8.3 Joint Distribution of the Sample Mean and Sample Variance 473

8.4 The t Distributions 480

8.5 Confidence Intervals 485

8.6 Bayesian Analysis of Samples from a Normal Distribution 495

8.7 Unbiased Estimators 506

8.8 Fisher Information 514

8.9 Supplementary Exercises 528

9 Testing Hypotheses 530

9.1 Problems of Testing Hypotheses 530

9.2 Testing Simple Hypotheses 550

9.3 Uniformly Most Powerful Tests 559

9.4 Two-Sided Alternatives 567

9.5 The t Test 576

9.6 Comparing the Means of Two Normal Distributions 587

9.7 The F Distributions 597

9.8 Bayes Test Procedures 605

9.9 Foundational Issues 617

9.10 Supplementary Exercises 621

10 Categorical Data and Nonparametric Methods 624

10.1 Tests of Goodness-of-Fit 624

10.2 Goodness-of-Fit for Composite Hypotheses 633

10.3 Contingency Tables 641

10.4 Tests of Homogeneity 647

10.5 Simpson’s Paradox 653

10.6 Kolmogorov-Smirnov Tests 657

10.7 Robust Estimation 666

10.8 Sign and Rank Tests 678

10.9 Supplementary Exercises 686

11 Linear Statistical Models 689

11.1 The Method of Least Squares 689

11.2 Regression 698

11.3 Statistical Inference in Simple Linear Regression 707

11.4 Bayesian Inference in Simple Linear Regression 729

11.5 The General Linear Model and Multiple Regression 736

11.6 Analysis of Variance 754

11.7 The Two-Way Layout 763

11.8 The Two-Way Layout with Replications 772

11.9 Supplementary Exercises 783

12 Simulation 787

12.1 What Is Simulation? 787

12.2 Why Is Simulation Useful? 791

12.3 Simulating Specific Distributions 804

12.4 Importance Sampling 816

12.5 Markov Chain Monte Carlo 823

12.6 The Bootstrap 839

12.7 Supplementary Exercises 850

Tables 853

Answers to Odd-Numbered Exercises 865

References 879

Index 885