A course in probability and statistics
著者
書誌事項
A course in probability and statistics
Duxbury Press, c1996
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注記
Includes index
内容説明・目次
内容説明
This author's modern approach is intended primarily for honors undergraduates or undergraduates with a good math background taking a mathematical statistics or statistical inference course. The author takes a finite-dimensional functional modeling viewpoint (in contrast to the conventional parametric approach) to strengthen the connection between statistical theory and statistical methodology.
目次
1. RANDOM VARIABLES AND THEIR DISTRIBUTION
Introduction / Sample Distributions / Distributions / Random Variables / Probability Functions and Density Functions / Distribution Functions and Quantiles / Univariate Transformations / Independence
2. EXPECTATION
Introduction / Properties of Expectation / Variance / Weak Law of Large Numbers Simulation and the Monte Carlo Method
3. SPECIAL CONTINUOUS MODELS
Gamma and Beta Distributions / The Normal Distribution / Normal Approximation and the Central Limit Theorem
4. SPECIAL DISCRETE MODELS
Combinatorics / The Binomial Distribution / The Multinomial Distribution / The Poisson Distribution / The Poisson Process
5. DEPENDENCE
Covariance, Linear Prediction, and Correlation / Multivariate Expectation / Covariance and Variance - Covariance Matrices / Multiple Linear Prediction / Multivariate Density Function / Invertible Transformations / The Multivariate Normal Distribution
6. CONDITIONAL DISTRIBUTIONS
Sampling Without Replacement / Hypergeometric Distribution / Conditional Density Functions / Conditional Expectation / Prediction / Conditioning and the Multivariate Normal Distribution / Random Parameters
7. NORMAL MODELS
Introduction / Chi-Square, t, and F Distribution / Confidence Intervals / The t Test of an Inequality / The t Test of an Equality
8. THE F TEST
Introduction to Linear Regression / The Method of Least Squares / Factorial Experiments / Input-Response and Experimental Models
9. LINEAR ANALYSIS
Linear Spaces / Identifiability / Saturated Spaces / Inner Products / Orthogonal Projections / Normal Equations
10. LINEAR REGRESSION
Least-Square Estimation / Sums of Squares / Distribution Theory / sugar Beet Experiment / Lube Oil Experiment / The t Test / Submodels / The F Test
11. ORTHOGONAL ARRAYS
Main Effects / Interactions / Experiments with Factors Having Three Levels / Randomization, Blocking, and Covariates
12. BINOMIAL AND POISSON MODELS
Nominal Confidence Intervals and Tests / Exact P-values / One-Parameter Exponential Families
13. LOGISTIC REGRESSION AND POISSON REGRESSION
Input-Response and Experimental Models / Maximum-Likelihood Estimation / Existence and Uniqueness of the Maximum-Likelihood Estimate / Interactively Reweighted Least-Squares Method / Normal Approximation / The Likelihood-Ratio Test / APPENDICES: A. PROPERTIES OF VECTORS AND MATRICES / B. SUMMARY OF PROBABILITY / C. SUMMARY OF STATISTICS / D. HINTS AND ANSWERS / E. TABLES / INDEX
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