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Mathematical Statistics and Data Analysis,9780534209346
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Mathematical Statistics and Data Analysis

by
Edition:
2nd
ISBN13:

9780534209346

ISBN10:
0534209343
Format:
Paperback
Pub. Date:
6/1/1994
Publisher(s):
Duxbury Press
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Summary

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

Table of Contents

Probability
1(32)
Introduction
1(1)
Sample Spaces
2(2)
Probability Measures
4(3)
Computing Probabilities: Counting Methods
7(8)
The Multiplication Principle
8(1)
Permutations and Combinations
9(6)
Conditional Probability
15(6)
Independence
21(3)
Concluding Remarks
24(1)
Problems
24(9)
Random Variables
33(36)
Discrete Random Variables
33(13)
Bernoulli Random Variables
35(1)
The Binomial Distribution
36(2)
The Geometric and Negative Binomial Distributions
38(1)
The Hypergeometric Distribution
39(2)
The Poisson Distribution
41(5)
Continuous Random Variables
46(11)
The Exponential Density
48(2)
The Gamma Density
50(3)
The Normal Distribution
53(4)
Functions of a Random Variable
57(4)
Concluding Remarks
61(1)
Problems
62(7)
Joint Distributions
69(42)
Introduction
69(2)
Discrete Random Variables
71(2)
Continuous Random Variables
73(10)
Independent Random Variables
83(2)
Conditional Distributions
85(7)
The Discrete Case
85(1)
The Continuous Case
86(6)
Functions of Jointly Distributed Random Variables
92(8)
Sums and Quotients
92(3)
The General Case
95(5)
Extrema and Order Statistics
100(3)
Problems
103(8)
Expected Values
111(52)
The Expected Value of a Random Variable
111(11)
Expectations of Functions of Random Variables
116(3)
Expectations of Linear Combinations of Random Variables
119(3)
Variance and Standard Deviation
122(7)
A Model for Measurement Error
126(3)
Covariance and Correlation
129(6)
Conditional Expectation and Prediction
135(7)
Definitions and Examples
135(5)
Prediction
140(2)
The Moment-Generating Function
142(7)
Approximate Methods
149(5)
Problems
154(9)
Limit Theorems
163(14)
Introduction
163(1)
The Law of Large Numbers
163(3)
Convergence in Distribution and the Central Limit Theorem
166(7)
Problems
173(4)
Distributions Derived from the Normal Distribution
177(8)
Introduction
177(1)
X2,t, and F Distributions
177(2)
The Sample Mean and the Sample Variance
179(3)
Problems
182(3)
Survey Sampling
185(54)
Introduction
185(1)
Population Parameters
186(2)
Simple Random Sampling
188(18)
The Expectation and Variance of the Sample Mean
189(7)
Estimation of the Population Variance
196(3)
The Normal Approximation to the Sampling Distribution of X
199(7)
Estimation of a Ratio
206(7)
Stratified Random Sampling
213(10)
Introduction and Notation
213(1)
Properties of Stratified Estimates
214(4)
Methods of Allocation
218(5)
Concluding Remarks
223(2)
Problems
225(14)
Estimation of Parameters and Fitting of Probability Distributions
239(60)
Introduction
239(1)
Fitting the Poisson Distribution to Emissions of Alpha Particles
239(4)
Parameter Estimation
243(3)
The Method of Moments
246(7)
The Method of Maximum Likelihood
253(20)
Maximum Likelihood Estimates of Multinomial Cell Probabilities
259(2)
Large Sample Theory for Maximum Likelihood Estimates
261(5)
Confidence Intervals for Maximum Likelihood Estimates
266(7)
Efficiency and the Cramer-Rao Lower Bound
273(7)
An Example: The Negative Binomial Distribution
277(3)
Sufficiency
280(5)
A Factorization theorem
281(3)
The Rao-Blackwell Theorem
284(1)
Concluding Remarks
285(1)
Problems
286(13)
Testing Hypotheses and Assessing Goodness of Fit
299(46)
Introduction
299(1)
The Neyman-Pearson Paradigm
300(3)
Optimal Tests: The Neyman-Pearson Lemma
303(3)
The Duality of Confidence Intervals and Hypothesis Tests
306(2)
Generalized Likelihood Ratio Tests
308(2)
Likelihood Ratio Tests for the Multinomial Distribution
310(6)
The Poisson Dispersion Test
316(2)
Hanging Rootograms
318(3)
Probability Plots
321(6)
Tests for Normality
327(3)
Concluding Remarks
330(1)
Problems
331(14)
Summarizing Data
345(42)
Introduction
345(1)
Methods Based on the Cumulative Distribution Function
346(11)
The Empirical Cumulative Distribution Function
346(2)
The Survival Function
348(5)
Quantile-Quantile Plots
353(4)
Histograms, Density Curves, and Stem-and-Leaf Plots
357(4)
Measures of Location
361(9)
The Arithmetic Mean
361(3)
The Median
364(1)
The Trimmed Mean
365(1)
M Estimates
366(1)
Comparison of Location Estimates
367(1)
Estimating Variability of Location Estimates by the Bootstrap
367(3)
Measures of Dispersion
370(2)
Boxplots
372(2)
Concluding remarks
374(1)
Problems
375(12)
Comparing Two samples
387(56)
Introduction
387(1)
Comparing Two Independent Samples
388(22)
Methods Based on the Normal Distribution
388(8)
An Example---A Study of Iron Retention
396(4)
Power
400(2)
A Nonparametric Method---the Mann-Whitney Test
402(8)
Comparing Paired Samples
410(7)
Methods Based on the Normal distribution
411(2)
A Nonparametric method---the signed Rank Test
413(2)
An Example---Measuring Mercury Levels in fish
415(2)
Experimental Design
417(7)
Mammary Artery Ligation
417(1)
The Placebo Effect
418(1)
The Lanarkshire Milk Experiment
419(1)
The Portocaval shunt
419(1)
FD&C Red No. 40
420(1)
Further Remarks on Randomization
421(1)
Observational Studies, Confounding, and Bias in Graduate Admissions
422(1)
Fishing Expeditions
423(1)
Concluding Remark
424(1)
Problems
425(18)
The Analysis of Variance
443(40)
Introduction
443(1)
The One-Way Layout
443(12)
Normal Theory; the F Test
445(6)
The Problem of Multiple Comparisons
451(1)
Tukey's Method
451(2)
The Bonferroni Method
453(1)
A Nonparametric Method---The Kruskal-Wallis Test
453(2)
The Two-Way Layout
455(16)
Additive Parametrization
455(3)
Normal theory for the Two-way Layout
458(7)
Randomized Block Designs
465(4)
A Nonparametric Method---Friedman's Test
469(2)
Concluding Remarks
471(1)
Problems
472(11)
The Analysis of Categorical Data
483(24)
Introduction
483(1)
Fisher's Exact Test
483(2)
The Chi-Square Test of Homogeneity
485(4)
The Chi-Square Test of Independence
489(3)
Matched-Pairs Designs
492(2)
Odds Ratios
494(4)
Concluding Remarks
498(1)
Problems
498(9)
Linear Least Squares
507(64)
Introduction
507(4)
Simple Linear Regression
511(18)
Statistical Properties of the Estimated Slope and Intercept
511(4)
Assessing the Fit
515(11)
Correlation and Regression
526(3)
The Matrix Approach to Linear Least Squares
529(3)
Statistical Properties of Least Squares Estimates
532(12)
Vector-Valued Random Variables
532(5)
Mean and Covariance of Least Squares Estimates
537(2)
Estimation of σ2
539(2)
Residuals and Standardized Residuals
541(1)
Inference about β
542(2)
Multiple Linear Regressions---An Example
544(4)
Conditional Inference, Unconditional Inference, and the Bootstrap
548(3)
Concluding Remarks
551(1)
Problems
552(19)
Decision Theory and Bayesian Inference
571(26)
Introduction
571(1)
Decision theory
571(16)
Bayes Rules and Minimax Rules
573(5)
Posterior Analysis
578(2)
Classification and Hypothesis Testing
580(4)
Estimation
584(3)
The Subjectivist Point of View
587(10)
Bayesian Inference for the Normal Distribution
589(3)
Bayesian Analysis for the Binomial Distribution
592(5)
Concluding Remarks
597(1)
Problems
597
Appendix A Common Distributions A1
Appendix B Tables A4
Bibliography A25
Answers to Selected Problems A31
Author Index A43
Index to Data Sets A45
Subject to Index A46


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