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What is included with this book?
1. PROBABILITY THEORY | |
Set Theory | |
Probability Theory | |
Conditional Probability and Independence | |
Random Variables | |
Distribution Functions | |
Density and Mass Functions | |
Exercises | |
Miscellanea | |
2. TRANSFORMATION AND EXPECTATIONS | |
Distribution of Functions of a Random Variable | |
Expected Values | |
Moments and Moment Generating Functions | |
Differentiating Under an Integral Sign | |
Exercises | |
Miscellanea | |
3. COMMON FAMILIES OF DISTRIBUTIONS | |
Introductions | |
Discrete Distributions | |
Continuous Distributions | |
Exponential Families | |
Locations and Scale Families | |
Inequalities and Identities | |
Exercises | |
Miscellanea | |
4. MULTIPLE RANDOM VARIABLES | |
Joint and Marginal Distributions | |
Conditional Distributions and Independence | |
Bivariate Transformations | |
Hierarchical Models and Mixture Distributions | |
Covariance and Correlation | |
Multivariate Distributions | |
Inequalities | |
Exercises | |
Miscellanea | |
5. PROPERTIES OF A RANDOM SAMPLE | |
Basic Concepts of Random Samples | |
Sums of Random Variables from a Random Sample | |
Sampling for the Normal Distribution | |
Order Statistics | |
Convergence Concepts | |
Generating a Random Sample | |
Exercises | |
Miscellanea | |
6. PRINCIPLES OF DATA REDUCTION | |
Introduction | |
The Sufficiency Principle | |
The Likelihood Principle | |
The Equivariance Principle | |
Exercises | |
Miscellanea | |
7. POINT EXTIMATION | |
Introduction | |
Methods of Finding Estimators | |
Methods of Evaluating Estimators | |
Exercises | |
Miscellanea | |
8. HYPOTHESIS TESTING | |
Introduction | |
Methods of Finding Tests | |
Methods of Evaluating Test | |
Exercises | |
Miscellanea | |
9. INTERVAL ESTIMATION | |
Introduction | |
Methods of Finding Interval Estimators | |
Methods of Evaluating Interval Estimators | |
Exercises | |
Miscellanea | |
10. ASYMPTOTIC EVALUATIONS | |
Point Estimation | |
Robustness | |
Hypothesis Testing | |
Interval Estimation | |
Exercises | |
Miscellanea | |
11. ANALYSIS OF VARIANCE AND REGRESSION | |
Introduction | |
One-way Analysis of Variance | |
Simple Linear Regression | |
Exercises | |
Miscellanea | |
12. REGRESSION MODELS | |
Introduction | |
Regression with Errors in Variables | |
Logistic Regression | |
Robust Regression | |
Exercises | |
Miscellanea | |
Appendix | |
Computer Algebra | |
References |