Continuous Univariate Distributions

Transcription

1 Continuous Univariate Distributions Volume 1 Second Edition NORMAN L. JOHNSON University of North Carolina Chapel Hill, North Carolina SAMUEL KOTZ University of Maryland College Park, Maryland N. BALAKRISHNAN McMaster University Hamilton, Ontario, Canada A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Brisbane Toronto Singapore

2 Contents Preface List of Tables xv xvii 12 Continuous Distributions (General) 1 1 Introduction, 1 2 Order Statistics, 6 3 Calculus of Probability Density Functions, 14 4 Systems of Distributions, Pearson System, Expansions, Transformed Distributions, Bessel Function Distributions, Miscellaneous, 53 5 Cornish-Fisher Expansions, 63 6 Note on Characterizations, 67 Bibliography, Normal Distributions 80 1 Definition and Tables, 80 2 Historical Remarks, 85 3 Moments and Other Properties, 88 4 Order Statistics, 93 5 Record Values, 99 6 Characterizations, Approximations and Algorithms, 111 vii

3 Viii CONTENTS 8 Estimation, Estimation of f, Estimation of a, Estimation of Functions of and a, Estimation from Censored Data, Siriiulational Algorithms, Box-Muller Method, Marsaglia-Bray's Improvement, Acceptance-Rejection Method, Ahrens-Dieter Method, Related Distributions, Truncated Normal Distributions, Mixtures, Other Related Distributions, 168 Bibliography, Lognormal Distributions Introduction, Historical Remarks, Moments and Other Properties, Estimation, Known, Unknown, Graphical Estimation, Tables and Graphs, Applications, Censoring, Truncated Lognormal and Related Distributions, Convolution of Normal and Lognormal Distributions, 247 Bibliography, Inverse Gaussian (Wald) Distributions Introduction, Genesis, Definition, Moments, Properties, Estimation of Parameters, 270

4 CONTENTS ix 7 Truncated Distributions Estimation of Parameters, Doubly Truncated Distribution, Truncation of the Lower Tail Only, Truncation of the Upper Tail Only, Conditional Expectations of the Estimators of the Cumulants, Related Distributions, Reciprocal of an Inverse Gaussian Variate, Birnbaum-Saunders Distribution, Generalized Inverse Gaussian Distributions, Mixtures of IG(/i, A) with Its Complementary Reciprocal, Other Related Distributions, Tables, Applications, 290 Bibliography, Cauchy Distribution Historical Remarks, Definition and Properties, Order Statistics, Methods of Inference, Methods Based on Order Statistics, Maximum Likelihood Inference, Conditional Inference, Bayesian Inference, Other Developments in Inference, Genesis and Applications, Characterizations, Generation Algorithms, Monahan's (1979) Algorithm, Kronmal and Peterson's (1981) Acceptance-Complement Method, Ahrens and Dieter's (1988) Algorithm, Related Distributions, 327 Bibliography, Gamma Distributions Definition, Moments and Other Properties, 338

5 X CONTENTS 3 Genesis and Applications, Tables and Computational Algorithms, Approximation and Generation of Gamma Random Variables, Characterizations, Estimation, Three Parameters Unknown, v Some Parameters Unknown, Estimation of Shape Parameter (j8 and y Known), Order Statistics and Estimators Based on Order Statistics, Related Distributions, Truncated Gamma Distributions, Compound Gamma Distributions, Transformed Gamma Distributions, Convolutions of Gamma Distributions, Mixtures of Gamma Distributions, Reflected Gamma Distributions, Generalized Gamma Distributions, 388 Bibliography, Chi-Square Distributions Including Chi and Rayleigh Historical Remarks, Definition, Moments and Other Properties, Tables and Nomograms, Approximations and Computational Algorithms, Characterizations, Simulational Algorithms, Distributions of Linear Combinations, Related Distributions, Specific Developments in the Rayleigh Distribution, Historical Remarks, Basic Properties, Order Statistics and Properties, Inference, Prediction, Record Values and Related Issues, 475

6 CONTENTS 10.7 Related Distributions, 479 Bibliography, Exponential Distributions Definition, Genesis, Some Remarks on History, Moments and Generating Functions, Applications, Order Statistics, Estimation, Classical Estimation, Grouped Data, Estimators Using Selected Quantiles, Estimation of Quantiles, Bayesian Estimation, Miscellaneous, Characterizations, Characterizations Based on Lack of Memory and on Distributions of Order Statistics, Characterizations Based on Conditional Expectations (Regression), Record Values, Miscellaneous, Stability, Mixtures of Exponential Distributions, Related Distributions, 551 Bibliography, Pareto Distributions, Introduction, Genesis, Definitions, Moments and Other Indices, Moments, Alternative Measures of Location, Measures of Inequality, 578

7 Xii CONTENTS 5 Estimation of Parameters, Least-Squares Estimators, Estimators from Moments, Maximum Likelihood Estimation, Estimation Based on Order Statistics, Sequential Estimation, Minimax Estimation, Estimation of Pareto Densities, 589 5:8 Estimation of Pareto Quantiles, Censored Data, Bayesian Estimation, Estimation of Lorenz Curve and Gini Index, Miscellaneous, Order Statistics and Record Values, Order Statistics, Record Values, Characterizations, Product and Ratios of Pareto Random Variables, Applications and Related Distributions, Generalized Pareto Distributions, 614 Bibliography, Weibull Distributions Historical Remarks, Definition, Order Statistics, Methods of Inference, Moment Estimation, Best Linear Unbiased Estimation, Asymptotic Best Linear Unbiased Estimation, Minimum Quantile Distance Estimation, Modified Moment Estimation, Maximum Likelihood Estimation, Modified Maximum Likelihood Estimation, Bayesian Estimation and Shrinkage Estimation, Tolerance Limits and Intervals, Prediction Limits and Intervals, Record Values, Tables and Graphs, 675

8 CONTENTS Xiii 9 Characterizations, Simulation Algorithms, Applications, Related Distributions, 686 Bibliography, 695 Abbreviations 723 Author Index 725 Subject Index 749