数理统计与应用：英文版

Preface
1 Introduction
1.1
Introduction
1.2
Combinatorial Methods
1.3
Binomial Coefficients
1.4
The Theory in Practice
2 Probability
2.1
Introduction
2.2
Sample Spaces
2.3
Events
2.4
The Probability of an Event
2.5
Some Rules of Probability
2.6
Conditional Probability
2.7
Independent Events
2.8
Bayes'' Theorem
2.9
The Theory in Practice
3 Probability Distributions and Probability Densities
3.1
Random Variables
3.2
Probability Distributions
3.3
Continuous Random Variables
3.4
Probability Density Functions
3.5
Multivariate Distributions
3.6
Marginal Distributions
3.7
Conditional Distributions
3.8
The Theory in Practice
4 Mathematical Expectation
4.1
Introduction
4.2
The Expected Value of a Random Variable
4.3
Moments
4.4
Chebyshev''s Theorem
4.5
Moment-Generating Functions
4.6
Product Moments
4.7
Moments of Linear Combinations of Random Variables
4.8
Conditional Expectations
4.9
The Theory in Practice
5 Special Probability Distributions
5.1
Introduction
5.2 The Discrete Uniform Distribution
5.3
The Bernoulli Distribution
5.4
The Binomial Distribution
5.5
The Negative Binomial and Geometric Distributions
5.6
The Hypergeometric Distribution
5.7
The Poisson Distribution
5.8
The Multinomial Distribution
5.9
The Multivariate Hypergeometric Distribution
5.10 The Theory in Practice
6 Special Probability Densities
6.1
Introduction
6.2
The Uniform Distribution
6.3
The Gamma, Exponential, and Chi-Square Distributions
6.4
The Beta Distribution
6.5
The Normal Distribution
6.6
The Normal Approximation to the Binomial Distribution
6.7
The Bivariate Normal Distribution
6.8
The Theory in Practice
7 Functions of Random Variables
7.1
Introduction
7.2
Distribution Function Technique
7.3
Transformation Technique: One Variable
7.4
Transformation Technique: Several Variables
7.5
Moment-Generating Function Technique
7.6
The Theory in Application
8 Sampling Distributions
8.1
Introduction
8.2
The Distribution of the Mean
8.3
The Distribution of the Mean: Finite Populations
8.4
The Chi-Square Distribution
8.5
The t Distribution
8.6
The F Distribution
8.7
Order Statistics
8.8
The Theory in Practice
9 Decision Theory
9.1
Introduction
9.2
The Theory of Games
9.3
Statistical Games
9.4
Decision Criteria
9.5
The Minimax Criterion
9.6
The Bayes Criterion
9.7
The Theory in Practice
10 Point Estimation
10.1 Introduction
10.2 Unbiased Estimators
10.3 Efficiency
10.4 Consistency
10.5 Sufficiency
10.6 Robustness
10.7 The Method of Moments
10.8 The Method of Maximum Likelihood
10.9 Bayesian Estimation
10.10 The Theory in Practice
11 Interval Estimation
11.1 Introduction
11.2 The Estimation of Means
11.3 The Estimation of Differences Between Means
11.4 The Estimation of Proportions
11.5 The Estimation of Differences Between Proportions
11.6 The Estimation of Variances
11.7 The Estimation of the Ratio of Two Variances
11.8 The Theory in Practice
12 Hypothesis Testing
12.1 Introduction
12.2 Testing a Statistical Hypothesis
12.3 Losses and Risks
12.4 The Neyman-Pearson Lemma
12.5 The Power Function of a Test
12.6 Likelihood Ratio Tests
12.7 The Theory in Practice
13 Tests of Hypothesis Involving Means, Variances,and Proportions
13.1 Introduction
13.2 Tests Concerning Means
13.3 Tests Concerning Differences Between Means
13.4 Tests Concerning Variances
13.5 Tests Concerning Proportions
13.6 Tests Concerning Differences Among k Proportions
13.7 The Analysis of an r x c Table
13.8 Goodness of Fit
13.9 The Theory in Practice
14 Regression and Correlation
14.1 Introduction
14.2 Linear Regression
14.3 The Method of Least Squares
14.4 Normal Regression Analysis
14.5 Normal Correlation Analysis
14.6 Multiple Linear Regression
14.7 Multiple Linear Regression Matrix Notation
14.8 The Theory in Practice
15 Design and Analysis of Experiments
15.1 Introduction
15.2 One-Way Designs
15.3 Randomized-Block Designs
15.4 Factorial Experiments
15.5 Multiple Comparisons
15.6 Other Experimental Designs
15.7 The Theory in Practice
16 Nonparametrie Tests
16.1 Introduction
16.2 The Sign Test
16.3 The Signed-Rank Test
16.4 Rank-Sum Tests: The U Test
16.5 Rank-Sum Tests: The H Test
16.6 Tests Based on Runs
16.7 The Rank Correlation Coefficient
16.8 The Theory in Practice
APPENDICES
A Sums and Products
A.1 Rules for Sums and Products
A.2 Special Sums
B Special Probability Distributions
B.1 Bernoulli Distribution
B.2 Binomial Distribution
B.3 Discrete Uniform Distribution Special Case
B.4 Geometric Distribution
B.5 Hypergeometric Distribution
B.6 Negative Binomial Distribution
B.7 Poisson Distribution
C Special Probability Densities
C.1 Beta Distribution
C.2 Cauchy Distribution
C.3 Chi-Square Distribution
C.4 Exponential Distribution
C.5 F Distribution
C.6 Gamma Distribution
C.7 Normal Distribution
C.8 t Distribution Student''s-t Distribution
C.9 Uniform Distribution Rectangular Distribution
Statistical Tables
Answers to Odd-Numbered Exercises
Index