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

Subject Matter

 * Statistics

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