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9780471183877

Continuous Multivariate Distributions, Volume 1 Models and Applications

by ; ;
  • ISBN13:

    9780471183877

  • ISBN10:

    0471183873

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2019-01-17
  • Publisher: Wiley-Interscience
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Summary

Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.

Author Biography

Norman L. Johnson, PhD, DSc, is Professor Emeritus in the Department of Statistics at the University of North Carolina at Chapel Hill.

Table of Contents

Preface xv
List of Tables
xix
List of Figures
xxi
Systems of Continuous Multivariate Distributions
1(104)
Introduction
1(3)
Historical Remarks
4(2)
Multivariate Generalization of Pearson System
6(4)
Series Expansions and Multivariate Central Limit Theorems
10(10)
Translation Systems
20(8)
Multivariate Linear Exponential-Type Distributions
28(2)
Sarmanov's Distributions
30(3)
Multivariate Linnik's Distributions
33(1)
Multivariate Kagan's Distributions
34(2)
Generation of Multivariate Nonnormal Random Variables
36(8)
Frechet Bounds
44(3)
Frechet, Plackett and Mardia's Systems
47(4)
Farlie-Gumbel-Morgenstern Distributions
51(11)
Multivariate Phase-Type Distributions
62(1)
Chebyshev-Type and Bonferroni Inequalities
63(4)
Singular Distributions
67(2)
Distributions with Almost-Lack of Memory
69(1)
Distributions with Specified Conditionals
70(3)
Distributions with Given Marginals
73(4)
Measures of Multivariate Skewness and Kurtosis
77(8)
Bibliography
85(20)
Multivariate Normal Distributions
105(146)
Introduction and Genesis
105(2)
Definition and Moments
107(4)
Other Properties
111(5)
Order Statistics
116(5)
Evaluation of Multivariate Normal Probabilities
121(24)
Reduction Formulas
125(2)
Orthant Probabilities
127(6)
Some Special Cases
133(6)
Approximations
139(6)
Quadrivariate Normal Orthant Probabilities
145(6)
Characterizations
151(10)
Estimation
161(39)
Estimation of ξ
161(17)
Estimation of V
178(4)
Estimation of Correlations
182(1)
Estimation Under Missing Data
183(4)
Estimation Under Special Structures
187(9)
Estimation of Functions of ξ and V
196(4)
Tolerance Regions
200(4)
Truncated Multivariate Normal Distributions
204(7)
Related Distributions
211(9)
Mixtures of Multivariate Normal Distributions
220(2)
Complex Multivariate Normal Distributions
222(29)
Bibliography
223(28)
Bivariate and Trivariate Normal Distributions
251(98)
Definition and Applications
251(1)
Historical Remarks
252(1)
Properties and Moments
253(11)
Bivariate Normal Integral-Tables and Approximations
264(13)
Characterizations
277(4)
Order Statistics
281(6)
Trivariate Normal Integral
287(6)
Estimation
293(18)
Bivariate Normal Distribution
293(17)
Trivariate Normal Distributions
310(1)
Truncated Bivariate and Trivariate Normal Distributions
311(9)
Dichotomized Variables
320(6)
Tetrachoic Correlation
320(4)
Biserial Correlation
324(2)
Related Distributions
326(5)
Mixtures of Bivariate Normal Distributions
326(1)
Bivariate Half Normal Distribution
326(1)
Distribution of Ratios
327(1)
``Bivariate Normal'' Distribution with Centered Normal Conditionals
328(3)
Bivariate Skew-Normal Distribution
331(18)
Bibliography
333(16)
Multivariate Exponential Distributions
349(82)
Introduction
349(1)
Bivariate Exponential Distributions
350(37)
Introduction
350(1)
Gumbel's Bivariate Exponentials
350(5)
Freund's Bivariate Exponential (Bivariate Exponential Mixture Distributions)
355(7)
Marshall and Olkin's Bivariate Exponential
362(7)
Friday and Patil's Bivariate Exponential
369(1)
Arnold and Strauss' Bivariate Exponential
370(1)
Moran and Downton's Bivariate Exponential
371(6)
Singpurwalla and Youngren's Bivariate Exponential
377(1)
Raftery's Bivariate Exponential
377(2)
Hayakawa's Bivariate Exponential
379(1)
Lindley and Singpurwalla's Bivariate Exponential Mixture
380(3)
Ghurye's Extended Bivariate Lack of Memory Distribution
383(2)
Cowan's Bivariate Exponential
385(1)
Infinite Divisibility
385(1)
Characterizations
386(1)
Multivariate Exponential Distributions
387(20)
Freund's Multivariate Exponential
388(3)
Marshall and Olkin's Multivariate Exponential
391(5)
Block and Basu's Multivariate Exponential
396(2)
Olkin and Tong's Multivariate Exponential
398(1)
Marshall and Olkin's Multivariate Exponential with Limited Memory
399(1)
Moran and Downton's Multivariate Exponential
400(1)
Raftery's Multivariate Exponential
401(2)
Krishnamoorthy and Parthasarathy's Multivariate Exponential
403(1)
Characterizations
403(4)
Multivariate Weibull Distributions
407(5)
Bivariate Distributions Induced by Frailties
412(19)
Bibliography
416(15)
Multivariate Gamma Distributions
431(54)
Introduction
431(1)
Bivariate Gamma Distributions
432(22)
McKay's Bivariate Gamma
432(1)
Cheriyan and Ramabhadran's Bivariate Gamma
432(4)
Kibble and Moran's Bivariate Gamma
436(1)
Sarmanov's Bivariate Gamma
437(1)
Jensen's Bivariate Gamma
438(2)
Royen's Bivariate Gamma
440(1)
Farlie--Gumbel--Morgenstern-Type Bivariate Gamma
441(1)
Prekopa and Szantai's Bivariate Gamma
442(1)
Smith, Adelfang and Tubb's Bivariate Gamma
443(2)
Dussauchoy and Berland's Bivariate Gamma
445(1)
Becker and Roux and Steel and le Roux's Bivariate Gamma
446(4)
Schmeiser and Lal's Bivariate Gamma
450(1)
Bivariate Chi-Square Distributions
451(3)
Multivariate Gamma Distributions
454(17)
Cheriyan and Ramabhadran's Multivariate Gamma
454(2)
Gaver's Multivariate Gamma
456(1)
Krishnamoorthy and Parthasarathy's Multivariate Gamma and Its Extension
457(1)
Prekopa and Szantai's Multivariate Gamma
458(1)
Kowalczyk and Tyrcha's Multivariate Gamma
459(2)
Royen's Multivariate Gamma
461(4)
Mathai and Moschopoulos's Multivariate Gamma
465(5)
Dussauchoy and Berland's Multivariate Gamma
470(1)
Multivariate (Jensen-Type) Chi-Square Distributions
471(4)
Noncentral Multivariate Chi-Square (Gamma) Distributions
475(2)
Infinite Divisibility of Multivariate Gamma
477(8)
Bibliography
478(7)
Dirichlet and Inverted Dirichlet Distributions
485(44)
Dirichlet Distributions
485(6)
Inverted Dirichlet Distribution
491(4)
Characteristic Functions
495(2)
Evaluation of Probability Integrals of Dirichlet Distributions
497(3)
Characterizations
500(4)
Estimation
504(3)
Applications
507(5)
Generalizations
512(17)
Generalized Dirichlet Distribution as a Prior for Multinomial Parameters
512(2)
Antelman's Generalization
514(1)
Johnson and Kotz's Generalization
515(1)
Delta-Dirichlet Distributions
515(4)
Connor and Mosimann's Generalization
519(4)
Bibliography
523(6)
Multivariate Liouville Distributions
529(22)
Introduction
529(1)
Definitions
530(1)
Properties
531(5)
Moments and Covariance Structure
536(2)
Characterizations
538(3)
Estimation and Applications
541(3)
Sign-Symmetric Dirichlet and Liouville Distributions
544(3)
Multivariate p-order Liouville Distributions
547(4)
Bibliography
548(3)
Multivariate Logistic Distributions
551(26)
Introduction
551(1)
Gumbel-Malik-Abraham Distribution
552(7)
Frailty and Archimedean Distributions
559(2)
Farlie--Gumbel--Morgenstern Distributions
561(1)
Differences of Extreme Value Variables
562(2)
Mixture Forms
564(1)
Geometric Minima and Maxima
565(3)
A General Flexible Model
568(1)
Conditionally Specified Logistic Model
569(1)
Some Other Generalizations
570(7)
Bibliography
573(4)
Multivariate Pareto Distributions
577(44)
Introduction
577(1)
Forms of Univariate Pareto Distributions
577(2)
Bivariate Pareto Distributions
579(20)
Bivariate Pareto of the First Kind
579(5)
Mardia's Bivariate Pareto of the Second Kind
584(1)
Bivariate Pareto of the Fourth Kind
585(2)
Conditionally Specified Bivariate Pareto
587(8)
Muliere and Scarsini's Bivariate Pareto
595(1)
Bilateral Bivariate Pareto
596(2)
Bivariate Semi-Pareto
598(1)
Multivariate Pareto Distributions
599(22)
Multivariate Pareto of the First Kind
599(3)
Multivariate Pareto of the Second Kind
602(3)
Multivariate Pareto of the Third Kind
605(1)
Multivariate Pareto of the Fourth Kind
606(5)
Conditionally Specified Multivariate Pareto
611(1)
Marshall-Olkin-Type Multivariate Pareto
612(2)
Multivariate Semi-Pareto
614(1)
Bibliography
615(6)
Bivariate and Multivariate Extreme Value Distributions
621(38)
General Bivariate Extreme Value Distributions
622(2)
Definition
622(1)
Properties
622(2)
Special Bivariate Extreme Value Distributions
624(16)
Type A Distributions
626(2)
Type B Distributions
628(1)
Type C Distributions
629(3)
Normal-Like Bivariate Extreme Value Distributions
632(5)
Estimation
637(3)
Multivariate Extreme Value Distributions
640(19)
Bibliography
652(7)
Natural Exponential Families
659(38)
Introduction
659(1)
Multivariate Natural Exponential Families
660(5)
Multivariate General Exponential Families
665(2)
Parameterization by the Mean and Steepness
667(2)
Variance Function
669(1)
Affine Transformations and Convolution: The Exponential Dispersion Model
670(3)
Some Statistical Results for NEFs
673(5)
Sufficiency, MLE, and UMVUE
673(2)
Cuts in NEFs
675(1)
Bayesian Theory
676(2)
NEFs with Quadratic Variance Function
678(19)
Morris Class
678(3)
Multivariate Case
681(8)
Characterizations
689(2)
Extensions
691(1)
Bibliography
691(6)
Author Index 697(16)
Subject Index 713

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