Introduction to Mathematical Statistics and Its Applications, An

by Larsen, Richard J.; Marx, Morris L.

• ISBN13: 9780131867932
• ISBN10: 0131867938
• Edition: 4th
• Format: Hardcover
• Copyright: 2006-01-01
• Publisher: Prentice Hall

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