An introduction to mathematical statistics and its applications
 Author/Creator
 Larsen, Richard J.
 Language
 English.
 Edition
 5th ed.
 Imprint
 Boston : Prentice Hall, c2012.
 Physical description
 x, 757 p. : ill. ; 26 cm.
Access
Available online

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QA276 .L314 2012
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QA276 .L314 2012

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QA276 .L314 2012
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Contributors
 Contributor
 Marx, Morris L.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 745751) and index.
 Contents

 1. Introduction 1.1 An Overview 1.2 Some Examples 1.3 A Brief History 1.4 A Chapter Summary 2. Probability 2.1 Introduction 2.2 Sample Spaces and the Algebra of Sets 2.3 The Probability Function 2.4 Conditional Probability 2.5 Independence 2.6 Combinatorics 2.7 Combinatorial Probability 2.8 Taking a Second Look at Statistics (Monte Carlo Techniques) 3. Random Variables 3.1 Introduction 3.2 Binomial and Hypergeometric Probabilities 3.3 Discrete Random Variables 3.4 Continuous Random Variables 3.5 Expected Values 3.6 The Variance 3.7 Joint Densities 3.8 Transforming and Combining Random Variables 3.9 Further Properties of the Mean and Variance 3.10 Order Statistics 3.11 Conditional Densities 3.12 MomentGenerating Functions 3.13 Taking a Second Look at Statistics (Interpreting Means) Appendix 3.A.1 MINITAB Applications 4. Special Distributions 4.1 Introduction 4.2 The Poisson Distribution 4.3 The Normal Distribution 4.4 The Geometric Distribution 4.5 The Negative Binomial Distribution 4.6 The Gamma Distribution 4.7 Taking a Second Look at Statistics (Monte Carlo Simulations) Appendix 4.A.1 MINITAB Applications Appendix 4.A.2 A Proof of the Central Limit Theorem 5. Estimation 5.1 Introduction 5.2 Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments 5.3 Interval Estimation 5.4 Properties of Estimators 5.5 MinimumVariance Estimators: The CramerRao Lower Bound 5.6 Sufficient Estimators 5.7 Consistency 5.8 Bayesian Estimation 5.9 Taking A Second Look at Statistics (Beyond Classical Estimation) Appendix 5.A.1 MINITAB Applications 6. Hypothesis Testing 6.1 Introduction 6.2 The Decision Rule 6.3 Testing Binomial DataH0: p = po 6.4 Type I and Type II Errors 6.5 A Notion of Optimality: The Generalized Likelihood Ratio 6.6 Taking a Second Look at Statistics (Statistical Significance versus "Practical" Significance) 7. Inferences Based on the Normal Distribution 7.1 Introduction 7.2 Comparing YA s/ vn and YA S/ vn 7.3 Deriving the Distribution of YA S/ vn 7.4 Drawing Inferences About A 7.5 Drawing Inferences About s2 7.6 Taking a Second Look at Statistics (Type II Error) Appendix 7.A.1 MINITAB Applications Appendix 7.A.2 Some Distribution Results for Y and S2 Appendix 7.A.3 A Proof that the OneSample t Test is a GLRT Appendix 7.A.4 A Proof of Theorem 7.5.2 8. Types of Data: A Brief Overview 8.1 Introduction 8.2 Classifying Data 8.3 Taking a Second Look at Statistics (Samples Are Not "Valid"!) 9. TwoSample Inferences 9.1 Introduction 9.2 Testing H0: A X =A Y 9.3 Testing H0: s2X=s2YThe F Test 9.4 Binomial Data: Testing H0: pX = pY 9.5 Confidence Intervals for the TwoSample Problem 9.6 Taking a Second Look at Statistics (Choosing Samples) Appendix 9.A.1 A Derivation of the TwoSample t Test (A Proof of Theorem 9.2.2) Appendix 9.A.2 MINITAB Applications 10. GoodnessofFit Tests 10.1 Introduction 10.2 The Multinomial Distribution 10.3 GoodnessofFit Tests: All Parameters Known 10.4 GoodnessofFit Tests: Parameters Unknown 10.5 Contingency Tables 10.6 Taking a Second Look at Statistics (Outliers) Appendix 10.A.1 MINITAB Applications 11. Regression 11.1 Introduction 11.2 The Method of Least Squares 11.3 The Linear Model 11.4 Covariance and Correlation 11.5 The Bivariate Normal Distribution 11.6 Taking a Second Look at Statistics (How Not to Interpret the Sample Correlation Coefficient) Appendix 11.A.1 MINITAB Applications Appendix 11.A.2 A Proof of Theorem 11.3.3 12. The Analysis of Variance 12.1 Introduction 12.2 The F Test 12.3 Multiple Comparisons: Tukey's Method 12.4 Testing Subhypotheses with Contrasts 12.5 Data Transformations 12.6 Taking a Second Look at Statistics (Putting the Subject of Statistics togetherthe Contributions of Ronald A. Fisher) Appendix 12.A.1 MINITAB Applications Appendix 12.A.2 A Proof of Theorem 12.2.2 Appendix 12.A.3 The Distribution of SSTR/(k1) SSE/(nk)When H1 is True 13. Randomized Block Designs 13.1 Introduction 13.2 The F Test for a Randomized Block Design 13.3 The Paired t Test 13.4 Taking a Second Look at Statistics (Choosing between a TwoSample t Test and a Paired t Test) Appendix 13.A.1 MINITAB Applications 14. Nonparametric Statistics 14.1 Introduction 14.2 The Sign Test 14.3 Wilcoxon Tests 14.4 The KruskalWallis Test 14.5 The Friedman Test 14.6 Testing for Randomness 14.7 Taking a Second Look at Statistics (Comparing Parametric and Nonparametric Procedures) Appendix 14.A.1 MINITAB Applications Appendix: Statistical Tables Answers to Selected OddNumbered Questions Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Noted for its integration of realworld data and case studies, this text offers sound coverage of the theoretical aspects of mathematical statistics. The authors demonstrate how and when to use statistical methods, while reinforcing the calculus that students have mastered in previous courses. Throughout theFifth Edition, the authors have added and updated examples and case studies, while also refining existing features that show a clear path from theory to practice.
(source: Nielsen Book Data)
Subjects
 Subject
 Mathematical statistics > Textbooks.
Bibliographic information
 Publication date
 2012
 Responsibility
 Richard J. Larsen, Morris L. Marx.
 Note
 Previous ed.: 2006.
 ISBN
 9780321693945
 0321693949
 9780321766564
 0321766563