Introduction to Mathematical Statistics and Its Applications, An,9780131867932

Introduction to Mathematical Statistics and Its Applications, An

by ;
Edition: 4th
ISBN13: 9780131867932
ISBN10: 0131867938
Format: Hardcover
Pub. Date: 2006-01-01
Publisher(s): Prentice Hall
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Summary

Noted for its integration of real-world data and case studies, this guide offers sound coverage of the theoretical aspects of mathematical statistics. It demonstrates how and when to use statistical methods, while reinforcing the calculus that readers have already mastered. Presents standard statistical techniques in a mathematical context, allowing the reader to see the underlying hypotheses for the applications. Uses case studies and practical worked-out examples to motivate statistical reasoning and demonstrate the application of statistical methods to a wide variety of real-world situations. Discusses practical problems in the application of the ideas covered in each chapter, as well as common misunderstandings or faulty approaches. Revised Minitab sections now conform to the Version 14, the latest release. For anyone interested in learning more about mathematical statistics.

Table of Contents

Preface vii
Introduction
1(20)
A Brief History
2(9)
Some Examples
11(9)
A Chapter Summary
20(1)
Probability
21(107)
Introduction
22(2)
Sample Spaces and the Algebra of Sets
24(12)
The Probability Function
36(6)
Conditional Probability
42(27)
Independence
69(16)
Combinatorics
85(28)
Combinatorial Probability
113(10)
Taking a Second Look at Statistics (Enumeration and Monte Carlo Techniques)
123(5)
Random Variables
128(146)
Introduction
129(1)
Binomial and Hypergeometric Probabilities
130(18)
Discrete Random Variables
148(13)
Continuous Random Variables
161(12)
Expected Values
173(20)
The Variance
193(10)
Joint Densities
203(17)
Combining Random Variables
220(6)
Further Properties of the Mean and Variance
226(14)
Order Statistics
240(9)
Conditional Densities
249(8)
Moment-Generating Functions
257(12)
Taking a Second Look at Statistics (Interpreting Means)
269(5)
Appendix 3.A.1 MINITAB Applications
271(3)
Special Distributions
274(69)
Introduction
275(1)
The Poisson Distribution
275(17)
The Normal Distribution
292(25)
The Geometric Distribution
317(5)
The Negative Binomial Distribution
322(5)
The Gamma Distribution
327(6)
Taking a Second Look at Statistics (Monte Carlo Simulations)
333(10)
Appendix 4.A.1 MINITAB Applications
337(4)
Appendix 4.A.2 A Proof of the Central Limit Theorem
341(2)
Estimation
343(84)
Introduction
344(2)
Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments
346(17)
Interval Estimation
363(16)
Properties of Estimators
379(15)
Minimum-Variance Estimators: The Cramer-Rao Lower Bound
394(4)
Sufficient Estimators
398(8)
Consistency
406(4)
Bayesian Estimation
410(13)
Taking a Second Look at Statistics (Revisiting the Margin of Error)
423(4)
Appendix 5.A.1 MINITAB Applications
424(3)
Hypothesis Testing
427(42)
Introduction
428(1)
The Decision Rule
428(12)
Testing Binomial Data---H0: p = po
440(6)
Type I and Type II Errors
446(16)
A Notion of Optimality: The Generalized Likelihood Ratio
462(4)
Taking a Second Look at Statistics (Statistical Significance versus ``Practical'' Significance)
466(3)
The Normal Distribution
469(53)
Introduction
470(1)
Comparing Y-μ/σ/√n and Y-μ/S/√n
470(3)
Deriving the Distribution of Y-μ/S/√n
473(8)
Drawing Inferences About μ
481(18)
Drawing Inferences About σ2
499(10)
Taking a Second Look at Statistics (``Bad'' Estimators)
509(13)
Appendix 7.A.1 MINITAB Applications
510(4)
Appendix 7.A.2 Some Distribution Results for Y and S2
514(2)
Appendix 7.A.3 A Proof of Theorem 7.5.2
516(3)
Appendix 7.A.4 A Proof that the One-Sample t Test Is a GLRT
519(3)
Types of Data: A Brief Overview
522(31)
Introduction
523(5)
Classifying Data
528(24)
Taking a Second Look at Statistics (Samples Are Not ``Valid'')
552(1)
Two-Sample Problems
553(45)
Introduction
554(1)
Testing H0: μx = μy -- The Two-Sample t Test
555(13)
Testing H0: σ2/y -- The F Test
568(8)
Binomial Data: Testing H0: px = py
576(6)
Confidence Intervals for the Two-Sample Problem
582(9)
Taking a Second Look at Statistics (Choosing Samples)
591(7)
Appendix 9.A.1 A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2)
593(2)
Appendix 9.A.2 MINITAB Applications
595(3)
Goodness-of-Fit Tests
598(48)
Introduction
599(1)
The Multinomial Distribution
599(7)
Goodness-of-Fit Tests: All Parameters Known
606(9)
Goodness-of-Fit Tests: Parameters Unknown
615(12)
Contingency Tables
627(13)
Taking a Second Look at Statistics (Outliers)
640(6)
Appendix 10.A.1 MINITAB Applications
644(2)
Regression
646(86)
Introduction
647(1)
The Method of Least Squares
647(30)
The Linear Model
677(25)
Covariance and Correlation
702(15)
The Bivariate Normal Distribution
717(8)
Taking a Second Look at Statistics (How Not to Interpret the Sample Correlation Coefficient)
725(7)
Appendix 11.A.1 MINITAB Applications
726(2)
Appendix 11.A.2 A Proof of Theorem 11.3.3
728(4)
The Analysis of Variance
732(40)
Introduction
733(2)
The F Test
735(12)
Multiple Comparisons: Tukey's Method
747(4)
Testing Subhypotheses with Contrasts
751(7)
Data Transformations
758(3)
Taking a Second Look at Statistics (Putting the Subject of Statistics Together---The Contributions of Ronald A. Fisher)
761(11)
Appendix 12.A.1 MINITAB Applications
762(4)
Appendix 12.A.2 A Proof of Theorem 12.2.2
766(1)
Appendix 12.A.3 The Distribution of SSTR/(k-1)/SSE/(n-k) When H1 Is True
767(5)
Randomized Block Designs
772(30)
Introduction
773(1)
The F Test for a Randomized Block Design
774(14)
The Paired t Test
788(8)
Taking a Second Look at Statistics (Choosing Between a Two-Sample t Test and a Paired t Test)
796(6)
Appendix 13.A.1 MINITAB Applications
800(2)
Nonparametric Statistics
802(48)
Introduction
803(1)
The Sign Test
804(6)
Wilcoxon Tests
810(16)
The Kruskal-Wallis Test
826(6)
The Friedman Test
832(3)
Testing for Randomness
835(6)
Taking a Second Look at Statistics (Comparing Parametric and Nonparametric Procedures)
841(9)
Appendix 14.A.1 MINITAB Applications
846(4)
Appendix: Statistical Tables 850(26)
Answers to Selected Odd-Numbered Questions 876(31)
Bibliography 907(8)
Index 915

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