Book:Alexander M. Mood/Introduction to the Theory of Statistics/Second Edition
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Alexander M. Mood and Franklin A. Graybill: Introduction to the Theory of Statistics (2nd Edition)
Published $\text {1963}$, McGraw-Hill
Subject Matter
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
Source work progress
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