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- Product code: 258476
- ISBN: 0495118680,
ISBN13: 9780495118688,
hardback
Published by Brooks Cole Rate this book...
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Description of Mathematical Statistics and Data Analysis |
This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts which are set in abstract settings.
Introduction to the bootstrap method as a simple yet powerful tool that is integrated with general inferential procedures (Monte Carlo methods are also introduced.)
Many exercises that enrich the book. (Some are relatively simple and reinforce calculations. Others concern bootstrap and Monte Carlo methods and theoretical material on survey sampling. Many incorporate use of the computer.)
New examples including interesting applications (e.g., probability of AIDS infection, state lotteries, polygraph testing) and graphical displays.
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Contents of Mathematical Statistics and Data Analysis |
1. PROBABILITY
Introduction / Sample Spaces / Probability Measures / Computer Probabilities: Counting Methods / Conditional Probability / Independence / Concluding Remarks / Problems
2. RANDOM VARIABLES
Discrete Random Variables / Continuous Random Variables / Functions of a Random Variable / Concluding Remarks / Problems
3. JOINT DISTRIBUTIONS
Introduction / Discrete Random Variables / Continuous Random Variables / Independent Random Variables / Conditional Distributions / Functions of Jointly Distributed Random Variables / Extreme and Order Statistics / Problems
4. EXPECTED VALUES
The Expected Value of a Random Variable / Variance and Standard Deviation / Covariance and Correlation / Conditional Expectation and Prediction / The Moment-Generating Function / Approximate Methods / Problems
5. LIMIT THEOREMS
Introduction / The Law of Large Number / Convergence in Distribution and the Central Limit Theorem / Problems
6. DISTRIBUTIONS DERIVED FROM THE NORMAL DISTRIBUTION
Introduction / Chi-Squared, t, and F Distributions / The Sample Mean and Sample Variance / Problems
7. SURVEY SAMPLING
Introduction / Production Parameters / Simple Random Sampling / Estimation of a Ratio / Stratified Random Sampling / Concluding Remarks / Problems
8. ESTIMATION OF PARAMETERS AND FITTING OF PROBABILITY DISTRIBUTIONS
Introduction / Fitting the Poisson Distribution to Emissions of Alpha Particles / Parameter Estimation / The Method of Moments / The Method of Maximum Likelihood / Efficiency and the Cramer-Rao Lower Bound / Sufficiency / Concluding Remarks / Problems
9. TESTING HYPOTHESES AND ASSESSING GOODNESS OF FIT
Introduction / The Neyman-Pearson Paradigm / Optimal Tests: The Neyman-Pearson Lemma / The Duality of Confidence Intervals and Hypothesis Tests / Generalized Likelihood Ratio Tests / Likelihood Ratio Tests for the Multinomial Distribution / The Poisson Dispersion Test / Hanging Rootograms / Probability Plots / Tests for Normality / Concluding Remarks / Problems
10. SUMMARIZING DATA
Introduction / Methods Based on the Cumulative Distribution Function / Histograms, Density Curves, and Stem-and-Leaf Plots / Measures of Location / Measures of Dispersion / Boxplots / Concluding Remarks / Problems
11. COMPARING TWO SAMPLES
Introduction / Comparing Two Independent Samples / Comparing Paired Samples / Experimental Design / Concluding Remarks / Problems
12. THE ANALYSIS OF VARIANCE
Introduction / The One-Way Layout / The Two-Way Layout / Concluding Remarks / Problems
13. THE ANALYSIS OF CATEGORICAL DATA
Introduction / Fisher's Exact Test / The Chi-Square Test of Homogeneity / The Chi-Square Test of Independence / Matched-Pair Designs / Odds Ratios / Concluding Remarks / Problems
14. LINEAR LEAST SQUARES
Introduction / Simple Linear Regression / The Matrix Approach to Linear Least Square / Statistical Properties of Least Squares Estimates / Multiple Linear Regression--An Example / Conditional Inference, Unconditional Inference, and the Bootstrap / Concluding Remarks / Problems
15. DECISION THEORY AND BAYESIAN INFERENCE
Introduction / Decision Theory / The Subjectivist Point of View / Concluding Remarks / Problems
APPENDIXES
A. COMMON DISTRIBUTIONS
B. TABLES
BIBLIOGRAPHY
ANSWERS TO SELECTED PROBLEMS
AUTHOR INDEX
INDEX TO DATA SETS
SUBJECT INDEX
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