An Introduction to Probability and Statistics.

Intro -- TITLE PAGE -- TABLE OF CONTENTS -- PREFACE TO THE THIRD EDITION -- PREFACE TO THE SECOND EDITION -- PREFACE TO THE FIRST EDITION -- ACKNOWLEDGMENTS -- ENUMERATION OF THEOREMS AND REFERENCES -- 1 PROBABILITY -- 1.1 INTRODUCTION -- 1.2 SAMPLE SPACE -- 1.3 PROBABILITY AXIOMS -- 1.4 COMBINATORICS: PROBABILITY ON FINITE SAMPLE SPACES -- 1.5 CONDITIONAL PROBABILITY AND BAYES THEOREM -- 1.6 INDEPENDENCE OF EVENTS -- 2 RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS -- 2.1 INTRODUCTION -- 2.2 RANDOM VARIABLES -- 2.3 PROBABILITY DISTRIBUTION OF A RANDOM VARIABLE -- 2.4 DISCRETE AND CONTINUOUS RANDOM VARIABLES -- 2.5 FUNCTIONS OF A RANDOM VARIABLE -- 3 MOMENTS AND GENERATING FUNCTIONS -- 3.1 INTRODUCTION -- 3.2 MOMENTS OF A DISTRIBUTION FUNCTION -- 3.3 GENERATING FUNCTIONS -- 3.4 SOME MOMENT INEQUALITIES -- 4 MULTIPLE RANDOM VARIABLES -- 4.1 INTRODUCTION -- 4.2 MULTIPLE RANDOM VARIABLES -- 4.3 INDEPENDENT RANDOM VARIABLES -- 4.4 FUNCTIONS OF SEVERAL RANDOM VARIABLES -- 4.5 COVARIANCE, CORRELATION AND MOMENTS -- 4.6 CONDITIONAL EXPECTATION -- 4.7 ORDER STATISTICS AND THEIR DISTRIBUTIONS -- 5 SOME SPECIAL DISTRIBUTIONS -- 5.1 INTRODUCTION -- 5.2 SOME DISCRETE DISTRIBUTIONS -- 5.3 SOME CONTINUOUS DISTRIBUTIONS -- 5.4 BIVARIATE AND MULTIVARIATE NORMAL DISTRIBUTIONS -- 5.5 EXPONENTIAL FAMILY OF DISTRIBUTIONS -- 6 SAMPLE STATISTICS AND THEIR DISTRIBUTIONS -- 6.1 INTRODUCTION -- 6.2 RANDOM SAMPLING -- 6.3 SAMPLE CHARACTERISTICS AND THEIR DISTRIBUTIONS -- 6.4 CHI-SQUARE, t-, AND F-DISTRIBUTIONS: EXACT SAMPLING DISTRIBUTIONS -- 6.5 DISTRIBUTION OF IN SAMPLING FROM A NORMAL POPULATION -- 6.6 SAMPLING FROM A BIVARIATE NORMAL DISTRIBUTION -- 7 BASIC ASYMPTOTICS: LARGE SAMPLE THEORY -- 7.1 INTRODUCTION -- 7.2 MODES OF CONVERGENCE -- 7.3 WEAK LAW OF LARGE NUMBERS -- 7.4 STRONG LAW OF LARGE NUMBERS† -- 7.5 LIMITING MOMENT GENERATING FUNCTIONS.

7.6 CENTRAL LIMIT THEOREM -- 7.7 LARGE SAMPLE THEORY -- 8 PARAMETRIC POINT ESTIMATION -- 8.1 INTRODUCTION -- 8.2 PROBLEM OF POINT ESTIMATION -- 8.3 SUFFICIENCY, COMPLETENESS AND ANCILLARITY -- 8.4 UNBIASED ESTIMATION -- 8.5 UNBIASED ESTIMATION (CONTINUED): A LOWER BOUND FOR THE VARIANCE OF AN ESTIMATOR -- 8.6 SUBSTITUTION PRINCIPLE (METHOD OF MOMENTS) -- 8.7 MAXIMUM LIKELIHOOD ESTIMATORS -- 8.8 BAYES AND MINIMAX ESTIMATION -- 8.9 PRINCIPLE OF EQUIVARIANCE -- 9 NEYMAN-PEARSON THEORY OF TESTING OF HYPOTHESES -- 9.1 INTRODUCTION -- 9.2 SOME FUNDAMENTAL NOTIONS OF HYPOTHESES TESTING -- 9.3 NEYMAN-PEARSON LEMMA -- 9.4 FAMILIES WITH MONOTONE LIKELIHOOD RATIO -- 9.5 UNBIASED AND INVARIANT TESTS -- 9.6 LOCALLY MOST POWERFUL TESTS -- 10 SOME FURTHER RESULTS ON HYPOTHESES TESTING -- 10.1 INTRODUCTION -- 10.2 GENERALIZED LIKELIHOOD RATIO TESTS -- 10.3 CHI-SQUARE TESTS -- 10.4 t-TESTS -- 10.5 F-TESTS -- 10.6 BAYES AND MINIMAX PROCEDURES -- 11 CONFIDENCE ESTIMATION -- 11.1 INTRODUCTION -- 11.2 SOME FUNDAMENTAL NOTIONS OF CONFIDENCE ESTIMATION -- 11.3 METHODS OF FINDING CONFIDENCE INTERVALS -- 11.4 SHORTEST-LENGTH CONFIDENCE INTERVALS -- 11.5 UNBIASED AND EQUIVARIANT CONFIDENCE INTERVALS -- 11.6 RESAMPLING: BOOTSTRAP METHOD -- 12 GENERAL LINEAR HYPOTHESIS -- 12.1 INTRODUCTION -- 12.2 GENERAL LINEAR HYPOTHESIS -- 12.3 REGRESSION ANALYSIS -- 12.4 ONE-WAY ANALYSIS OF VARIANCE -- 12.5 TWO-WAY ANALYSIS OF VARIANCE WITH ONE OBSERVATION PER CELL -- 12.6 TWO-WAY ANALYSIS OF VARIANCE WITH INTERACTION -- 13 NONPARAMETRIC STATISTICAL INFERENCE -- 13.1 INTRODUCTION -- 13.2 U-STATISTICS -- 13.3 SOME SINGLE-SAMPLE PROBLEMS -- 13.4 SOME TWO-SAMPLE PROBLEMS -- 13.5 TESTS OF INDEPENDENCE -- 13.6 SOME APPLICATIONS OF ORDER STATISTICS -- 13.7 ROBUSTNESS -- FREQUENTLY USED SYMBOLS AND ABBREVIATIONS -- REFERENCES -- STATISTICAL TABLES -- ANSWERS TO SELECTED PROBLEMS -- AUTHOR INDEX.

SUBJECT INDEX -- WILEY SERIES IN PROBABILITY AND STATISTICS -- END USER LICENSE AGREEMENT.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.