# Book:Alexander M. Mood/Introduction to the Theory of Statistics/Second Edition

## Alexander M. Mood and Franklin A. Graybill: Introduction to the Theory of Statistics (2nd Edition)

Published $\text {1963}$, McGraw-Hill.

### Contents

Preface to the First Edition
Preface to the Second Edition
Chapter 1. Introduction
1.1. Statistics
1.2. The Scope of This Book
1.3. Reference system
1.4. Bibliography
Chapter 2. Probability
2.1. Introduction
2.2. Classical or A Priori Probability
2.3. A Posteriori or Frequency Probability
2.4. Probability Models
2.5. Point Sets
2.6. The Axiomatic Development of Probability
2.7. Discrete Sample Space with a Finite Number of Points
2.8. Permutations and Combinations
2.9. Sibling's Formula
2.10. Sum and Product Notations
2.11. The Binomial and Multinomial theorems
2.12. Combinatorial Generating Functions
2.13. Marginal Probability
2.14. Conditional Probability
2.15. Two Basic Laws of Probability
2.16. Compound Events
2.17. Independence
2.18. Random Variables
2.19. Problems
2.20. Bibliography
Chapter 3. Discrete Random Variables
3.1. Introduction
3.2. Discrete Density Functions
3.3. Multivariate Distributions
3.4. The Binomial Distribution
3.5. The Multinomial Distribution
3.6. The Poisson Distribution
3.7. Other Discrete Distributions
3.8. Problems
3.9. Bibliography
Chapter 4. Continuous Random Variables
4.1. Introduction
4.2. Continuous Random Variables
4.3. Multivariate Distributions
4.4. Cumulative Distributions
4.5. Marginal Distributions
4.6. Conditional Distributions
4.7. Independence
4.8. Random Sample
4.9. Derived Distributions
4.10. Problems
4.11. Bibliography
Chapter 5. Expected Values and Moments
5.1. Expected Values
5.2. Moments
5.3. Moment Generating Functions
5.4. Moments for Multivariate Distributions
5.5. The Moment Problem
5.6. Conditional Expectations
5.7. Problems
5.8. Bibliography
Chapter 6. Special Continuous Distributions
6.1. Uniform Distribution
6.2. The Normal Distribution
6.3. The Gamma Distribution
6.4. The Beta Distribution
6.5. Other Distribution Functions
6.6. Complete Density Functions
6.7. Problems
6.8. Bibliography
Chapter 7. Sampling
7.1. Inductive Inference
7.2. Populations and Samples
7.3. Sample Distributions
7.4. Sample Moments
7.5. The Law of Large Numbers
7.6. The Central-limit Theorem
7.7. Normal Approximation to the Binomial Distribution
7.8. Role of the Normal Distribution in Statistics
7.9. Problems
7.10. Bibliography
Chapter 8. Point Estimation
8.1. Decision Theory
8.2. Point Estimation
8.3. Sufficient Statistics; Single-parameter Case
8.4. Sufficient Statistics; More than One Parameter
8.5. Unbiased
8.6. Consistent Estimator
8.7. Asymptotically Efficient Estimators
8.8. Minimum-variance Unbiased Estimators
8.9. Principle of Maximum Likelihood
8.10. Some Maximum-likelihood Estimators
8.11. Properties of Maximum-likelihood Estimators
8.12. Estimation by the Method of Moments
8.13. Bayes Estimators
8.14. Problems
8.15. Bibliography
Chapter 9. The Multivariate Normal Distribution
9.1. The Bivariate Normal Distribution
9.2. Matrices and Determinants
9.3. Multivariate Normal
9.4. Problems
9.5. Bibliography
Chapter 10. Sampling Distributions
10.1. Distributions of Functions of Random Variables
10.2. Distribution of the Sample Mean for Normal Densities
10.3. The Chi-square Distribution
10.4. Independence of the Sample Mean and Variance for Normal Densities
10.5. The $F$ Distribution
10.6. "Student's" $t$ Distribution
10.7. Distribution of Sample Means for Binomial and Poisson Densities
10.8. Large-sample Distribution of Maximum-likelihood Estimators
10.9. Distribution of Order Statistics
10.10. Studentized Range
10.11. Problems
10.12. Bibliography
Chapter 11. Interval Estimation
11.1. Confidence Intervals
11.2. Confidence Intervals for the Mean of a Normal Distribution
11.3. Confidence Intervals for the Variance of a Normal Distribution
11.4. Confidence Region for Mean and Variance of a Normal Distribution
11.5. A General Method for Obtaining Confidence Intervals
11.6. Confidence Intervals for the Parameter of a Binomial Distribution
11.7. Confidence Intervals for Large Samples
11.8. Confidence Regions for Large Samples
11.9. Multiple Conhdence Intervals
11.10. Problems
11.11. Bibliography
Chapter 12. Tests of Hypotheses
12.1. Introduction
12.2. Test of a Simple Hypothesis against a Simple Alternative
12.3. Composite Hypotheses
12.4. Tests of $\theta < \theta_1$ versus $\theta > \theta_1$ for Densities with a Single Parameter $\theta$
12.5. Tests of Hypothesis $H_1: \theta_1 \le \theta \le \theta_2$ with the Alternative Hypothesis $H_2: \theta > \theta_2, \theta < \theta_1$
12.6. Generalized Likelihood-ratio Test
12.7. Tests on the Mean of a Normal Population
12.8. The Difference between Means of Two Normal Populations
12.9. Tests on the Variance of a Normal Distribution
12.10. The Goodness-of-fit Test
12.11. Tests of Independence in Contingency Tables
12.12. Problems
12.13. Bibliography
Chapter 13. Regression and Linear Hypotheses
13.1. Introduction
13.2. Simple Linear Models
13.3. Prediction
13.4. Discrimination
13.5. Point Estimation Case B
13.6. The General Linear Model
13.7. Problems
13.8. Bibliography
Chapter 14. Experimental Design Models
14.1. Introduction
14.2. Experimental Design Model
14.3. One-way Classification Model
14.4. Two-way Classification Model
14.5. Other Models
14.6. Problems
14.7. Bibliography
Chapter 15. Sequential Tests of Hypotheses
15.1. Sequential Analysis
15.2. Construction of Sequential Tests
15.3. Power Functions
15.4. Average Sample Size
15.5. Sampling Inspection
15.6. Sequential Sampling Inspection
15.7. Sequential Test for the Mean of a Normal Population
15.8. Problems
15.9. Bibliography
Chapter 16. Nonparametric Methods
16.1. Introduction
16.2. A Basic Distribution
16.3. Location and Dispersion
16.4. Comparison of Two Populations
16.5. Tolerance Limits
16.6. Rank Test for Two Samples
16.7. Asymptotic Efficiencies and the Randomization Test
16.8. Problems
16.9. Bibliography
Tables
I. Ordinates of the Normal Density Function
II. Cumulative Normal Distribution
III. Cumulative Chi-square Distribution
IV. Cumulative "student's" Distribution
V. Cumulative $F$ Distribution
VI. Upper 1 Per Cent Points of the Studentized Range
VII. Upper 5 Per Cent Points of the Studentized Range
VIII. Upper 10 Per Cent Points of the Studentized Range
Index

Next