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书名： Continuous Multivariate Distributions: Models and Applications，第二版
作者：
SECOND EDITION
SAMUEL KOTZ
N. BALAKRISHNAN
NORMAN L. JOHNSON



Systems of Continuous Multivariate Distributions
1 Introduction, 1
2 Historical Remarks, 4
3 Multivariate Generalization of Pearson System, 6
4 Series Expansions and Multivariate Central Limit
Theorems, 10
5 Translation Systems, 20
6 Multivariate Linear Exponential－τ'ype Distributions, 28
7 Sarmanov’s Distributions, 30
8 Multivariate Linnik's Distributions, 33
9 Multivariate Kagan、Distributions, 34
10 Generation of Multivariate Nonnormal Random
Variables, 36
11 Frechet Bounds, 44
12 Frechet, Plackett and Mardia’s Systems, 47
13 Farlie-Gumbel-Morgenstern Distributions, 51
14 Multivariate Phase-Type Distributions, 62
15 Chebyshev-Type and Bonferroni Inequalities, 63
16 Singular Distributions, 67
1 7 Distributions with Almost-Lack of Memory, 69
18 Distributions with Specified Conditionals, 70
19 Distributions with Given Marginals, 73
20 Measures of Multivariate Skewness and Kurtosis, 77
xv
XIX
XX45 Multivariate Normal Distributions 105
1 Introduction and Genesis, 105
2 Definition and Moments, 107
3 Other Properties, 111
4 Order Statistics, 116
5 Evaluation of Multivariate Normal Probabiliti臼， 121
5.1 Reduction Formulas, 125
5.2 Orthant Probabilities, 127
5.3 Some Special Cases, 133
5.4 Approximations, 139
6 Quadrivariate Normal Orthant Probabilities, 145
7 Characterizations, 151
8 Estimation, 161
8.1 Estimation of ι161
8.2 Estimation of V, 178
8.3 Estimation of Correlations, 182
8.4 Estimation Under Missing Data, 183
8.5 Estimation Under Special Structures, 187
8.6 Estimation of Functions of e and V, 196
9 Tolerance Regions, 200
10 Truncated Multivariate Normal Distributions, 204
11 Related Distributions, 211
12 Mixtures of Multivariate Normal Distributions, 220
13 Complex Multivariate Normal Distributions, 222
Bibliography, 223
46 Bivariate and Tri variate Normal Distributions 251
1 Definition and Applications, 251
2 Historical Remarks, 252
3 Properties and Moments, 253
4 Bivariate Normal Integral-Tables and
Approximations, 264
5 Characterizations, 277
6 Order Statistics, 281
7 Trivariate Normal Integral, 287
CONTENTS
8 Estimation, 293
8.1 Bivariate Normal Distribution, 293
8.2τ'rivariate Normal Distributions, 310
9τ'runcated Bivariate and τ'rivariate Normal
Distributions, 311
10 Dichotomized Variables, 320
10.1 Tetrachoric Correlation, 320
10.2 Biserial Correlation, 324
11 Related Distributions, 326
11.1 Mixtures of Bivariate Normal Distributions, 326
11.2 Bivariate Half Normal Distribution, 326
11.3 Distribution of Ratios, 327
11.4 "Bivariate Normal" Distri bu ti on with
Centered Normal Conditionals, 328
11.5 Bivariate Skew-Normal Distribution, 331
Bibliography, 333
4 7 Multivariate Exponential Distributions
1 Introduction, 349
2 Bivariate Exponential Distributions, 350
2.1 Introduction, 350
2.2 Gumbel's Bivariate Exponentials, 350
2.3 Freund’s Bivariate Exponential (Bivariate
Exponential Mixture Distributio叫， 355
2.4 Marshall and Olkin's Bivariate Exponential, 362
2.5 Friday and Patil's Bivariate Exponential, 369
2.6 Arnold and Strauss’ Bivariate Exponential, 370
2. 7 Moran and Downton's Bivariate Exponential, 371
2.8 Singpurwalla and Youngren's Bivariate
Exponential, 377
2.9 Raftery's Bivariate Exponential, 377
2.10 Hayakawa's Bivariate Exponential, 379
2.11 Lindley and Singpurwalla’s Bivariate
Exponential Mixture, 380
2.12 Ghurye's Extended Bivariate Lack
of Memory Distribution, 383
2.13 Cowan's Bivariate Exponential, 385
2.14 Infinite Divisibility, 385
2.15 Characterizations, 386
IX
349
x CONTENTS
3 Multivariate Exponential Distributions, 387
3.1 Freund's Multivariate Exponential, 388
3.2 Marshall and Olkin's Multivariate Exponential, 391
3.3 Block and Basu、Multivariate Exponential, 396
3.4 Olkin and Tong’s Multivariate Exponential, 398
3.5 Marshall and Olkin's Multivariate Exponential
with Limited Memory, 399
3.6 Moran and Downton's Multivariate Exponential, 400
3.7 Raftery's Multivariate Exponential, 401
3.8 Krishnamoorthy and Parthasarathy's
Multivariate Exponential, 403
3.9 Characterizations, 403
4 Multivariate Weibull Distributions, 407
5 Bivariate Distributions Induced by Frailties, 412
Bibliography, 416
48 Multivariate Gamma Distributions
1 Introduction, 431
2 Bivariate Gamma Distributions, 432
2.1 McK町’s Bivariate Gamma, 432
2.2 Cheriyan and Ramabhadran、Bivariate G缸丑ma, 432
2.3 Kibble and Moran's Bivariate Gamma, 436
2.4 Sarmanov's Bivariate Gamma, 437
2.5 Jensen、Bivariate Gamma, 438
2.6 Royen、Bivariate Gamma, 440
2. 7 Farlie-Gumbel-Morgenstern－τ'ype Bivariate
Gamma, 441
2.8 Prekopa and Sz缸itai's Bivariate G缸丑ma, 442
2.9 Smith, Adelfang and τ飞ibb’s Bivariate
Gamma, 443
2.10 Dussauchoy and Berland’s Bivariate Gamma, 445
2.11 Becker and Roux and Steel and le Roux's
Bivariate Gamma, 446
2.12 Schmeiser and Lal’s Bivariate Gamma, 450
2.13 Bivariate Chi-Square Distributions, 451
3 Multivariate Gamma Distributions, 454
431
3.1 Cheriyan and Ramabhadran's Multivariate Gamma, 454
3.2 Gaver’s Multivariate Gamma, 456
3.3 Krishnamoorthy and Parthasarathy's Multivariate
Gamma and Its Extension, 457
CONTENTS
3.4 Prekopa and Szantai’s Multivariate Gamma, 458
3.5 Kowalczyk and Tyrcha’s Multivariate Gamma, 459
3.6 Royen’s Multivariate Gamma, 461
3. 7 Mathai and Moschopoulos’s Multivariate Gamma, 465
3.8 Dussauchoy and Berland’s Multivariate Gamma, 470
4 Multivariate (Jensen-Type) Chi-Square
Distributions, 471
5 None .仕tral Multivariate Chi-Square (Gamma)
Distributions, 4 75
6 Infinite Divisibility of Multivariate Gamma, 477
Bibliography, 478
49 Dirichlet and Inverted Dirichlet Distributions
1 Dirichlet Distributions, 485
2 Inverted Dirichlet Distribution, 491
3 Characteristic Functions, 495
4 Evaluation of Probability Integrals of Dirichlet
Distributions, 497
5 Characterizations, 500
6 Estimation, 504
7 Applications, 507
8 Generalizations, 512
8.1 Generalized Dirichlet Distribution as a Prior for
Multinomial Parameters, 512
8.2 Antelman、Generalization, 514
8.3 Johnson and Kotz’s Generalization, 515
8.4 Delta-Dirichlet Distributions, 515
8.5 Connor and Mosimann、Generalization, 519
Bibliography, 523
50 Multivariate Liouville Distributions
1 Introduction, 529
2 Definitions, 530
3 Properties, 531
4 Moments and Covariance Structure, 536
5 Characterizations, 538
6 Estimation and Applications, 541
xi
485
529
Xll CONTENTS
7 Sign-Symmetric Dirichlet and Liouville
Distributions, 544
8 Multivariate p-order Liouville Distributions, 547
Bibliography, 548
51 Multivariate Logistic Distributions
1 Introduction, 551
2 Gumbel-Malik-Abraham Distribution, 552
3 Frailty and Archimedean Distributions, 559
4 Farlie-Gumbel-Morgenstern Distributions, 561
5 Differences of Extreme Value Variables, 562
6 Mixture Forms, 564
7 Geometric Minima and Maxima, 565
8 A General Flexible Model, 568
9 Conditionally Specified Logistic Model, 569
10 Some Other Generalizations, 570
Bibliography, 573
52 Multivariate Pareto Distributions
1 Introduction, 577
2 Forms of Univariate Pareto Distributions, 577
3 Bivariate Pareto Distributions, 579
3.1 Bivariate Pareto of the First Kind, 579
3.2 Mardia's Bivariate Pareto of the Second Kind, 584
3.3 Bivariate Pareto of the Fourth Kind, 585
3.4 Conditionally Specified Bivariate Pareto, 587
3.5 Muliere and Scarsini’s Bivariate Pareto, 595
3.6 Bilateral Bivariate Pareto, 596
3.7 Bivariate Semi-Pareto, 598
4 Multivariate Pareto Distributions, 599
4.1 Multivariate Pareto of the First Kind, 599
4.2 Multivariate Pareto of the Second Kind, 602
4.3 Multivariate Pareto of the Third Kind, 605
4.4 Multivariate Pareto of the Fourth Kind, 606
4.5 Conditionally Specified Multivariate Pareto, 611
4.6 Marshall-Olkin-Type Multivariate Pareto, 612
4.7 Multivariate Semi-Pareto, 614
551
577
CONTENTS
Bibliography, 615
53 Bivariate and Multivariate Extreme Value
Distributions
1 General Bivariate Extreme Value Distributions, 622
1.1 Definition, 622
1.2 Properties, 622
2 Special Bivariate Extreme Value Distributions, 624
2.1 Type A Distributions, 626
2.2τ'ype B Distributions, 628
2.3τ'ype C Distributions, 629
2.4 Normal-Like Bivariate Extreme Value
Distributions, 632
2.5 Estimation, 637
3 Multivariate Extreme Value Distributions, 640
Bibliography, 652
54 Natural Exponential Families
1 Introduction, 659
2 Multivariate Natural Exponential Families, 660
3 Multivariate General Exponential Families, 665
4 Parameterization by the Mean and Steepn臼s, 667
5 Variance Function, 669
6 Affineτransformations and Convolution:
The Exponential Dispersion Model, 670
7 Some Statistical Results for NEFs, 673
7.1 Sufficiency, MLE, and UMVUE, 673
7.2 Cuts in NEFs, 675
7.3 Bayesian Theory, 676
8 NEFs with Quadratic Variance Function, 678
8.1 Morris Cl出s, 678
8.2 Multivariate Case, 681
8.3 Characterizations, 689
8.4 Extensions, 691
Bibliography, 691
Author Index
Subject Index
·..
Xlll
621
659
697
713