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概率统计：英文版
作者：（美）Charles J.Stone著
出版社：机械工业出版社
出版时间：2003-07-01
ISBN：9787111123200
定价：¥89.00
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内容简介
本书是以作者在加利福尼亚大学伯克利分校统计学系给高年级本科生和研究生授课的教学讲义为基础写成的，前半部分为概率，后半部分为统计。书中的主要内容包括概率、随机变量及其分布、期望连续及离散模型、独立性、条件概率分布、密度函数及期望、线性分析，线性回归、泊松分布、逻辑回归及泊松回归等。 尽管本书的重点是使读者对主要概念有个全面的理解，但它同时还向读者介绍了实际数据分析的方方面面。本书适合作为高等院校数学及相关专业高年级本科生或研究生概率统计课程的教材，同时也可作为相关领域科技人员的参考资料。 全新的教学方法·与现代数值逼近方法和数值分析的其他方面相适应·加强统计理论、方法论及应用之间的联系·在线性模型及广义线性模型的处理中，省略重复的矩阵运算，强调概念理解。
作者简介
CharlesJ.Stone，斯坦福大学统计学博士，现为加利福尼亚大学伯克利分校统计系教授，主要研究方向是非参数统计模型、统计软件。
目录
CHAPTER 1 Random Variables and Their Distributions 1
1.1 Introduction 1
1.2 Sample Distributions 5
1.3 Distributions 14
1.4 Random Variables 23
1.5 Probability Functions and Density Functions 33
1.6 Distribution Functions and Quantiles 45
1.7 Univariate Transformations 60
1.8 Independence 69
CHAPTER 2 Expectation 81
2.1 Introduction 81
2.2 Properties of Expectation 91
2.3 Variance 99
2.4 Weak Law of Large Numbers 110
2.5 Simulation and the Monte Carlo Method 121
CHAPTER 3 Special Continuous Models 134
3.1 Gamma and Beta Distributions 134
3.2 The Normal Distribution 145
3.3 Normal Approximation and the Central Limit Theorem
CHAPTER 4 Special Discrete Models 162
4.1 Combinatorics ' 162
4.2 The Binomial Distribution 172
4.3 The Multinomial Distribution 188
4.4 The Poisson Distribution 195
4.5 The Poisson Process 204
CHAPTER 5 Dependence 209
5.1 Covariance, Linear Prediction, and Correlation 209
5.2 Multivariate Expectation 219
5.3 Covariance and Variance-Covariance Matrices 225
5.4 Multiple Linear Prediction 236
5.5 Multivariate Density Functions 242
5.6 Invertible Transformations 252
5.7 The Multivariate Normal Distribution 263
CHAPTER 6 Conditioning 274
6.1 Conditional Distributions 274
6.2 Sampling Without Replacement 285
6.3 Hypergeometric Distribution 292
6.4 Conditional Density Functions 300
6.5 Conditional Expectation 307
6.6 Prediction 316
6.7 Conditioning and the Multivariate Normal Distribution 322
6.8 Random Parameters 330
CHAPTER 7 Normal Models 338
7.1 Introduction 338
7.2 Chi-Square, t, and F Distributions 344
7.3 Confidence Intervals 353
7.4 The t Test of an Inequality 365
7.5 The t Test of an Equality 375
7.6 The F Test 388
CHAPTER 8 Introduction to Linear Regression 396
8.1 The Method of Least Squares 396
8.2 Factorial Experiments 407
8.3 Input-Response and Experimental Models 415
CHAPTER 9 Linear Analysis 427
9.1 Linear Spaces 427
9.2 Identifiability 438
9.3 Saturated Spaces 447
9.4 Inner Products 454
9.5 Orthogonal Projections 470
9.6 Normal Equations 485
CHAPTER 10 Linear Regression 494
10.1 Least-Squares Estimation 494
10.2 Sums of Squares 506
10.3 Distribution Theory 515
10.4 Sugar Beet Experiment 526
10.5 Lube Oil Experiment 538
10.6 The t Test 552
10.7 Submodels 560
10.8 The F Test 568
CHAPTER 11 Orthogonal Arrays 579
11.1 Main Effects 579
11.2 Interactions 595
11.3 Experiments with Factors Having Three Levels' 611
11.4 Randomization, Blocking, and Covariates 620
CHAPTER 12 Binomial and Poisson Models 635
12.1 Nominal Confidence Intervals and Tests 636
12.2 Exact P-Values 651
12.3 One-Parameter Exponential Families 662
CHAPTER 13 Logistic Regression and Poisson Regression 673
13.1 Input-Response and Experimental Models 675
13.2 Maximum-Likelihood Estimation 686
13.3 Existence and Uniqueness of the Maximum-Likelihood Estimate 699
13.4 Iteratively Reweighted Least-Squares Method 709
13.5 Normal Approximation 723
13.6 The Likelihood-Ratio Test 736
APPENDIX A Properties of Vectors and Matrices 751
APPENDIX B Summary of Probability 760
B.1 Random Variables and Their Distributions 760
B.2 Random Vectors 769
APPENDIX C Summary of Statistics 774
C.1 Normal Models 774
C.2 Linear Regression 779
C.3 Binomial and Poisson Models 785
C.4 Logistic Regression and Poisson Regression 787
APPENDIX D Hints and Answers 798
APPENDIX E Tables 828
Index 833
1.1 Introduction 1
1.2 Sample Distributions 5
1.3 Distributions 14
1.4 Random Variables 23
1.5 Probability Functions and Density Functions 33
1.6 Distribution Functions and Quantiles 45
1.7 Univariate Transformations 60
1.8 Independence 69
CHAPTER 2 Expectation 81
2.1 Introduction 81
2.2 Properties of Expectation 91
2.3 Variance 99
2.4 Weak Law of Large Numbers 110
2.5 Simulation and the Monte Carlo Method 121
CHAPTER 3 Special Continuous Models 134
3.1 Gamma and Beta Distributions 134
3.2 The Normal Distribution 145
3.3 Normal Approximation and the Central Limit Theorem
CHAPTER 4 Special Discrete Models 162
4.1 Combinatorics ' 162
4.2 The Binomial Distribution 172
4.3 The Multinomial Distribution 188
4.4 The Poisson Distribution 195
4.5 The Poisson Process 204
CHAPTER 5 Dependence 209
5.1 Covariance, Linear Prediction, and Correlation 209
5.2 Multivariate Expectation 219
5.3 Covariance and Variance-Covariance Matrices 225
5.4 Multiple Linear Prediction 236
5.5 Multivariate Density Functions 242
5.6 Invertible Transformations 252
5.7 The Multivariate Normal Distribution 263
CHAPTER 6 Conditioning 274
6.1 Conditional Distributions 274
6.2 Sampling Without Replacement 285
6.3 Hypergeometric Distribution 292
6.4 Conditional Density Functions 300
6.5 Conditional Expectation 307
6.6 Prediction 316
6.7 Conditioning and the Multivariate Normal Distribution 322
6.8 Random Parameters 330
CHAPTER 7 Normal Models 338
7.1 Introduction 338
7.2 Chi-Square, t, and F Distributions 344
7.3 Confidence Intervals 353
7.4 The t Test of an Inequality 365
7.5 The t Test of an Equality 375
7.6 The F Test 388
CHAPTER 8 Introduction to Linear Regression 396
8.1 The Method of Least Squares 396
8.2 Factorial Experiments 407
8.3 Input-Response and Experimental Models 415
CHAPTER 9 Linear Analysis 427
9.1 Linear Spaces 427
9.2 Identifiability 438
9.3 Saturated Spaces 447
9.4 Inner Products 454
9.5 Orthogonal Projections 470
9.6 Normal Equations 485
CHAPTER 10 Linear Regression 494
10.1 Least-Squares Estimation 494
10.2 Sums of Squares 506
10.3 Distribution Theory 515
10.4 Sugar Beet Experiment 526
10.5 Lube Oil Experiment 538
10.6 The t Test 552
10.7 Submodels 560
10.8 The F Test 568
CHAPTER 11 Orthogonal Arrays 579
11.1 Main Effects 579
11.2 Interactions 595
11.3 Experiments with Factors Having Three Levels' 611
11.4 Randomization, Blocking, and Covariates 620
CHAPTER 12 Binomial and Poisson Models 635
12.1 Nominal Confidence Intervals and Tests 636
12.2 Exact P-Values 651
12.3 One-Parameter Exponential Families 662
CHAPTER 13 Logistic Regression and Poisson Regression 673
13.1 Input-Response and Experimental Models 675
13.2 Maximum-Likelihood Estimation 686
13.3 Existence and Uniqueness of the Maximum-Likelihood Estimate 699
13.4 Iteratively Reweighted Least-Squares Method 709
13.5 Normal Approximation 723
13.6 The Likelihood-Ratio Test 736
APPENDIX A Properties of Vectors and Matrices 751
APPENDIX B Summary of Probability 760
B.1 Random Variables and Their Distributions 760
B.2 Random Vectors 769
APPENDIX C Summary of Statistics 774
C.1 Normal Models 774
C.2 Linear Regression 779
C.3 Binomial and Poisson Models 785
C.4 Logistic Regression and Poisson Regression 787
APPENDIX D Hints and Answers 798
APPENDIX E Tables 828
Index 833
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