Continuous multivariate distributions: 1 Models and applications
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Edition: | 2nd ed. |
| Series: | Univariate discrete distributions
Wiley series in probability and statistics : Applied probability and statistics section |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009529733&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Rev. ed. of: Continuous multivariate distributions / Norman L. Johnson, Samuel Kotz, 1972 |
| Physical Description: | XXII, 722 S. graph. Darst. |
| ISBN: | 0471183873 |
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| adam_text | Contents
Preface
xv
List of Tables
xix
List of Figures
xxi
44
Systems of Continuous Multivariate Distributions
1
1
Introduction,
1
2
Historical Remarks,
4
3
Multivariate Generalization of Pearson System,
б
4
Series Expansions and Multivariate Central Limit
Theorems,
10
5
Translation Systems,
20
6
Multivariate Linear Exponential-Type Distributions,
28
7
Sarmanov s Distributions,
30
8
Multivariate Linnik s Distributions,
33
9
Multivariate Kagan s Distributions,
34
10
Generation of Multivariate
Nonnormal
Random
Variables,
36
11
Fréchet
Bounds,
44
12
Fréchet, 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
17
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
viii CONTENTS
Bibliography,
85
45
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 Probabilities,
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
£, 161
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
£
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 Trivariate 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 ix
8
Estimation,
293
8.1 Bivariate Normal Distribution, 293
8.2 Trivariate Normal
Distributions,
310
9
Truncated
Bivariate and Trivariate 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 Distribution with
Centered Normal Conditionals,
328
11.5
Bivariate Skew-Normal Distribution,
331
Bibliography,
333
47
Multivariate Exponential Distributions
349
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 Distributions)
, 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
χ
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 s 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
Divariate
Distributions Induced by Frailties,
412
Bibliography,
416
48
Multivariate Gamma Distributions
431
1
Introduction,
431
2
Bivariate Gamma Distributions,
432
2.1
McKay s Bivariate Gamma,
432
2.2
Cheriyan and Ramabhadran s Bivariate Gamma,
432
2.3
Kibble and Moran s Bivariate Gamma,
436
2.4
Sarmanov s Bivariate Gamma,
437
2.5
Jensen s Bivariate Gamma,
438
2.6
Royen s Bivariate Gamma,
440
2.7
Farlie-Gumbel-Morgenstern-Type Bivariate
Gamma,
441
2.8
Prekopa
and
Szántai s
Bivariate Gamma,
442
2.9
Smith,
Adelfang
and Tubb 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 Lai s Bivariate Gamma,
450
2.13
Bivariate Chi-Square Distributions,
451
3
Multivariate Gamma Distributions,
454
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 xi
3.4
Prekopa
and Szántai 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
Noncentral
Multivariate Chi-Square (Gamma)
Distributions,
475
6
Infinite Divisibility of Multivariate Gamma,
477
Bibliography,
478
49
Dirichlet and Inverted Dirichlet Distributions
485
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 s Generalization,
514
8.3
Johnson and Kotz s Generalization,
515
8.4
Delta-Dirichlet Distributions,
515
8.5
Connor and Mosimann s Generalization,
519
Bibliography,
523
50
Multivariate Liouville Distributions
529
1
Introduction,
529
2
Definitions,
530
3
Properties,
531
4
Moments and Covariance Structure,
536
5
Characterizations,
538
6
Estimation and Applications,
541
xii CONTENTS
7
Sign-Symmetric
Dirichlet and Liouville
Distributions,
544
8 Multivariate p-order Liouville
Distributions,
547
Bibliography,
548
51
Multivariate Logistic Distributions
551
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
577
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
CONTENTS xiii
Bibliography,
615
53 Bivariate and Multivariate Extreme
Value
Distributions
621
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
2.2
Type
В
Distributions,
628
2.3
Type
С
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
659
1
Introduction,
659
2
Multivariate Natural Exponential Families,
660
3
Multivariate General Exponential Families,
665
4
Parameterization by the Mean and Steepness,
667
5
Variance Function,
669
6 Affine
Transformations 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 Class,
678
8.2
Multivariate Case,
681
8.3
Characterizations,
689
8.4
Extensions,
691
Bibliography,
691
Author Index
697
Subject Index
713
|
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| id | DE-604.BV013925931 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:56:00Z |
| institution | BVB |
| isbn | 0471183873 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009529733 |
| oclc_num | 174949476 |
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| physical | XXII, 722 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley |
| record_format | marc |
| series2 | Univariate discrete distributions Wiley series in probability and statistics : Applied probability and statistics section |
| spellingShingle | Kotz, Samuel 1930-2010 Balakrishnan, Narayanaswamy 1956- Johnson, Norman Lloyd 1917-2004 Continuous multivariate distributions Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Multivariate Analyse (DE-588)4040708-1 gnd Multivariate Wahrscheinlichkeitsverteilung (DE-588)4205373-0 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4040708-1 (DE-588)4205373-0 |
| title | Continuous multivariate distributions |
| title_auth | Continuous multivariate distributions |
| title_exact_search | Continuous multivariate distributions |
| title_full | Continuous multivariate distributions 1 Models and applications Samuel Kotz ; N. Balakrishnan ; Norman L. Johnson |
| title_fullStr | Continuous multivariate distributions 1 Models and applications Samuel Kotz ; N. Balakrishnan ; Norman L. Johnson |
| title_full_unstemmed | Continuous multivariate distributions 1 Models and applications Samuel Kotz ; N. Balakrishnan ; Norman L. Johnson |
| title_short | Continuous multivariate distributions |
| title_sort | continuous multivariate distributions models and applications |
| topic | Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Multivariate Analyse (DE-588)4040708-1 gnd Multivariate Wahrscheinlichkeitsverteilung (DE-588)4205373-0 gnd |
| topic_facet | Wahrscheinlichkeitsverteilung Multivariate Analyse Multivariate Wahrscheinlichkeitsverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009529733&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013925927 |
| work_keys_str_mv | AT kotzsamuel continuousmultivariatedistributions1 AT balakrishnannarayanaswamy continuousmultivariatedistributions1 AT johnsonnormanlloyd continuousmultivariatedistributions1 |
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| Call Number: |
0048 MAT 627f 2005 A 7488(2)
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| Copy 1 | On permanent loan Ausgeliehen – Due: 31.12.9999 |
Branch Library Mathematics & Informatics
| Call Number: |
0102 MAT 627f 2005 A 7488
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| Copy 1 | Available for loan On Shelf |
| Copy 2 | Available for loan On Shelf |