Introduction to the Theory of Statistics

PART I: PROBABILITY

Chapter 1. Introduction and Summary
Chapter 2. Kinds of Probability
Chapter 3. Probability-Axiomatic


PART II: RANDOM VARIABLES, DISTRIBUTION FUNCTIONS, AND EXPECTATION

Chapter 1. Introduction and Summary
Chapter 2. Random Variable and Cumulative Distribution Function
Chapter 3. Density Functions
Chapter 4. Expectations and Moments


PART III: SPECIAL PARAMETRIC FAMILITES OF UNIVARIATE DISTRIBUTIONS

Chapter 1. Introduction and Summary
Chapter 2. Discrete Distributions
Chapter 3. Continuous Distributions
Chapter 4. Comments

PART IV. JOINT AND CONDITIONAL DISTRIBUTIONS, STOCHASTIC INDEPENDENCE,MORE EXCEPTION

Chapter 1. Introduction and Summary
Chapter 2. Joint Distibution Functions
Chapter 3. Conditional Distributions and Stochastic Independence
Chapter 4. Expectation
Chapter 5. Bivariate Normal Distribution


PART V: DISTRIBUTIONS OF FUNCTIONS AND RANDOM VARIABLES

Chapter 1. Introduction and Summary
Chapter 2. Expectations of Functions of Random Variables
Chatper 3. Cumulative-Distribution-Function Technique
Chapter 4. Moment-Generating-Function Technique
Chapter 5. The Transformation Y=g(x)
Chapter 6. Transformations

PART VI: SAMPLING AND SAMPLING DISTRIBUTIONS

Chapter 1. Introduction and Summary
Chapter 2. Sampling
Chapter 3. Sample Mean
Chapter 4. Sampling from the Normal Distributions
Chapter 5. Order Statistics


PART VII: PARAMETRIC POINT ESTIMATION

Chapter 1. Introduction and Summary
Chapter 2. Methods of Finding Estimators
Chapter 3. Properties of Point Estimators
Chapter 4. Sufficiency
Chapter 5. Unbiased Estimation
Chapter 6. Location or Scale Invariance
Chapter 7. Bayes Estimators
Chapter 8. Vector of Parameters
Chapter 9. Optimum Properties of Maximum-likelihood Estimation


PART VIII: Parametric Interval Estimation

Chapter 1. Introduction and Summary
Chapter 2. Confidence Intervals
Chapter 3. Sampling from the Normal Distribution
Chapter 4. Methods of Finding Confidence Intervals
Chapter 5. Large-Sample Confidence Intervals
Chapter 6. Bayesian Interval Estimates


PART IX: TESTS OF HYPOTHESES

Chapter 1. Introduction and Summary
Chapter 2. Simple Hypothesis versus Simple Alternative
Chapter 3. Composite Hypotheses
Chapter 4. Tests of Hypotheses-Sampling from the National Distribution
Chapter 5. Chi-Square Tests
Chapter 6. Tests of Hypotheses and Confidence Intervals
Chapter 7. Sequential Tests of Hypotheses


PART X: LINEAR MODELS

Chapter 1. Introduction and Summary
Chapter 2. Examples of the Linear Model
Chapter 3. Definition of Linear Model
Chapter 4. Point Estimation-Case A
Chapter 5. Confidence Intervals-Case A
Chapter 6. Tests of Hypotheses-Case A
Chapter 7. Point Estimation-Case B


PART XI: NONPARAMETRIC METHOD

Chapter 1. Introduction and Summary
Chapter 2. Inferences Concerning a Cumulative Distribution Function
Chapter 3. Inferences Concerning Quantiles
Chapter 4. Tolerance Limits
Chapter 5. Equality of Two Distributions