Continuous Univariate Distributions
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1 Continuous Univariate Distributions Volume 2 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 xiii xv 22 Extreme Value Distributions 1 1 Genesis, 1 2 Introduction, 2 3 Limiting Distributions of Extremes, 4 4 Distribution Function and Moments, 11 5 Order Statistics, 15 6 Record Values, 17 7 Generation, Tables, and Probability Paper, 23 8 Characterizations, 25 9 Methods of Inference, Moment Estimation, Simple Linear Estimation, Best Linear Unbiased (Invariant) Estimation, Asymptotic Best Linear Unbiased Estimation, Linear Estimation with Polynomial Coefficients, Maximum Likelihood Estimation, Conditional Method, Method of Probability-Weighted Moments, "Block-Type" Estimation, A Survey of Other Developments, Tolerance Limits and Intervals, Prediction Limits and Intervals, Outliers and Robustness, Probability Plots, Modifications, and Model Validity, 66 vii
3 iii CONTENTS 14 Applications, Generalized Extreme Value Distributions, Other Related Distributions, 86 References, Logistic Distribution Historical Remarks and Genesis, Definition, Generating Functions and Moments, Properties, Order Statistics, Methods of Inference, Record Values, Tables, Applications, Generalizations, Related Distributions, 147 References, Laplace (Double Exponential) Distributions Definition, Genesis, and Historical Remarks, Moments, Generating Functions, and Properties, Order Statistics, Methods of Inference, Maximum Likelihood Estimation, Best Linear Unbiased Estimation, Simplified Linear Estimation, Asymptotic Best Linear Unbiased Estimation, Conditional Inference, Other Developments, Tolerance Limits and Prediction Intervals, Related Distributions, Applications, 201 References, Beta Distributions Definition, Genesis and Random Number Generation, Properties, 217
4 CONTENTS IX 4 Estimation, Applications, Approximations and Tables, Approximations, Tables, Related Distributions, Products, Quotients, and Differences of Independent Beta Variables, 256 References, Uniform (Rectangular) Distributions Definition, Genesis, Historical Remarks, Generating Functions, Moments, and Order Statistics, Characterizations, Estimation of Parameters, Estimation Using Order Statistics Censored Samples, Tables of Random Numbers, Related Distributions, Mixtures of Two Uniform Distributions, Other Related Distributions, Applications, Corrections for Grouping, Life Testing, Traffic Flow Applications, Applications in Statistical Tests and Models, Random Number Generation, 312 References, F-Distributions Introduction, Properties, Order Statistics, Tables, Approximations and Nomograms, Applications, 343
5 * CONTENTS 7 Pearson Type VI Distributions, Other Related Distributions, "Generalized" /-"-Distributions, Other Related Distributions, 350 References, (-Distributions Genesis and Historical Remarks, Properties, Tables and Nomograms, Tables, Nomograms, Approximations, Applications, Pearson Type VII Distributions and Their Modifications, Other Related Distributions, 403 References, Noncentral x ^Distributions Definition and Genesis, Historical Notes, Distribution, Moments, Properties of the Distribution, Estimation, Tables and Computer Algorithms, Approximations, Applications, Related Distributions, 470, References, Noncentral ^-Distributions Definition and Genesis, Historical Remarks, Properties, Tables and Computer Programs, Tables, Computer Programs, 489
6 CONTENTS xi 5 Approximations, Estimation of the Noncentrality Parameter A,, Related Distributions, Doubly Noncentral /-"-Distributions, Noncentral Beta Distributions, 502 References, Noncentral (-Distributions Definition, Historical Remarks, Applications and Estimation, Moments, Distribution Function, Approximations, Tables, Charts, and Computer Algorithms, Related Distributions, Noncentral Beta Distribution, Doubly Noncentral /-Distribution, Modified Noncentral (-Distribution, Distribution of Noncentral (-Statistic When the Population is Nonnormal, 538 References, Distributions of Correlation Coefficients Introduction and Genesis, Derivation of Distribution of R, Historical Remarks, Distribution of R in Non-normal Populations and Robustness, Tables and Approximations (Asymptotic Expansions), Tables, Approximations Using Transforms, Asymptotic Expansions of the Distribution of R, Estimation of p: Additional Robustness Considerations, General Remarks, Point Estimation, Maximum Likelihood Estimation, 590
7 XII CONTENTS 6.4 Estimation of Common p Based on Several Samples, Miscellaneous Estimation Problems, Sample Covariance, Circular Serial Correlation, Noncircular Serial Correlation, Leipnik Distribution, Multiple Correlation Coefficient, 617 References, Lifetime Distributions and Miscellaneous Orderings Introduction, Life Distributions, Birnbaum-Saunders Distributions and Transformations, Ordering and Classification of Distributions, Basic Definitions and Bounds, Reliability Classification of Orderings, Alternative Stochastic Classification of Orderings, 672 References, 681 Abbreviations 691 Author Index 693 Subject Index 711
Continuous Univariate Distributions
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