Multivariate t-distributions and their applications:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XII, 272 S. graph. Darst. |
| ISBN: | 0521826543 |
Staff View
MARC
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| 245 | 1 | 0 | |a Multivariate t-distributions and their applications |c Samuel Kotz ; Saralees Nadarajah |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
| 300 | |a XII, 272 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804132742185615360 |
|---|---|
| adam_text | Contents
List of Illustrations page
ix
Preface
xi
1
Introduction
1
1.1
Definition
1
1.2
Representations
2
1.3
Characterizations
7
1.4
A Closure Property
8
1.5
A Consistency Property
9
1.6
Density Expansions
9
1.7
Moments
10
1.8 Maximums 12
1.9
Distribution of a Linear Function
15
1.10
Marginal Distributions
15
1.11
Conditional Distributions
16
1.12
Quadratic Forms
19
1.13
F
Matrix
20
1.14
Association
20
1.15
Entropy
21
1.16
Kullback-Leibler Number
23
1.17
Rényi
Information
26
1.18
Identities
30
1.19
Some Special Cases
33
2
The Characteristic Function
36
2.1
Sutradhars Approach
36
2.2
Joarder and Ali s Approach
38
2.3
Levy Representation
41
3
Linear Combinations, Products, and Ratios
44
3.1
Linear Combinations
44
3.2
Products
52
3.3
Ratios
56
v
vi
Contents
4
Divariate
Generalizations and Related Distributions
63
4.1
Owen s
Noncentral
Bivariate
t
Distribution
63
4.2
Siddiqui s
Noncentral
Bivariate
t
Distribution
66
4.3
Patii
and Liao s
Noncentral
Bivariate
t
Distribution
68
4.4
Krishnan s
Noncentral
Bivariate
t
Distribution
69
4.5
Krishnan s Doubly
Noncentral
Bivariate
t
Distribution
71
4.6
Bulgren
et al. s
Bivariate
í
Distribution
72
4.7
Siotani s
Noncentral
Bivariate
t
Distribution
73
4.8
Tiku
and Kambo s Bivariate
t
Distribution
74
4.9
Conditionally Specified Bivariate
t
Distribution
76
4.10
Jones Bivariate
t
Distribution
80
5
Multivariate Generalizations and Related Distributions
87
5.1
Kshirsagar s
Noncentral
Multivariate
t
Distribution
87
5.2
Miller s
Noncentral
Multivariate
t
Distribution
90
5.3
Stepwise Multivariate
í
Distribution
90
5.4
Siotani s
Noncentral
Multivariate
t
Distribution
93
5.5
Arellano-
Valle
and Bolfarine s Generalized
t
Distribution
94
5.6
Fang
et al. s
Asymmetric Multivariate
í
Distribution
97
5.7
Gupta s Skewed Multivariate
t
Distribution
98
5.8
Sahu
et al. s
Skewed Multivariate
t
Distribution
102
5.9
Azzalini and Capitanio s Skewed Multivariate
í
Distribution
103
5.10
Jones Skewed Multivariate
t
Distribution
105
5.11
Matrix-
Variate
í
Distribution
112
5.12
Complex Multivariate
t
Distribution
119
5.13
Steyn s
Nonnormal
Distributions
120
5.14
Inverted Dirichlet Distribution
126
6
Probability Integrals
127
6.1
Dunnett and Sobel s Probability Integrals
127
6.2
Gupta and Sobel s Probability Integrals
131
6.3
John s Probability Integrals
135
6.4
Amos and Bulgren s Probability Integrals
137
6.5 Steffens
Noncentral
Probabilities
139
6.6
Dutt s Probability Integrals
140
6.7
Amos Probability Integral
143
6.8
Fujikoshi s Probability Integrals
144
6.9
Probabilities of Cone
145
6.10
Probabilities of Convex Polyhedra
148
6.11
Probabilities of Linear Inequalities
158
6.12
Maximum Probability Content
160
6.13
Monte Carlo Evaluation
161
7
Probability Inequalities
165
7.1
Dunnett and Sobel s Probability Inequalities
165
7.2
Dunn s Probability Inequalities
169
Contents
vii
7.3 Halperin s
Probability Inequalities
170
7.4
Sidák s
Probability Inequalities
171
7.5
Tong s Probability Inequalities
172
8
Percentage Points
174
8.1
Dunnett and Sobel s Percentage Points
174
8.2
Krishnaiah and Armitage s Percentage Points
175
8.3
Gupta
et al. s
Percentage Points
176
8.4 Rausch
and Horn s Percentage Points
176
8.5 Hahn
and Hendrickson s Percentage Points
177
8.6
Siotani s Percentage Points
177
8.7
Graybill and Bowden s Percentage Points
178
8.8
Pillai
and Ramachandran s Percentage Points
180
8.9
Dunnett s Percentage Points
180
8.10
Gupta and Sobel s Percentage Points
181
8.11
Chen s Percentage Points
182
8.12
Bowden and Graybill s Percentage Points
183
8.13
Dunnett and Tamhane s Percentage Points
183
8.14
Kwong and Liu s Percentage Points
187
8.15
Other Results
187
9
Sampling Distributions
191
9.1
Wishart
Matrix
191
9.2
Multivariate
t
Statistic
198
9.3
Hotelling s T2 Statistic
199
9.4
Entropy and Kullback-Leibler Number
204
10
Estimation
207
10.1
Tiku
and Kambo s Estimation Procedure
207
10.2
ML Estimation via EM Algorithm
210
10.3
Missing Data Imputation
212
10.4
Laplacian T-Approximation
214
10.5
Sutradhar s Score Test
215
10.6
Multivariate
í
Model
219
10.7
Generalized Multivariate
t
Model
222
10.8
Simulation
223
11
Regression Models
228
11.1
Classical Linear Model
228
11.2
Bayesian Linear Models
233
11.3
Indexed Linear Models
235
11.4
General Linear Model
237
11.5
Nonlinear Models
239
12
Applications
241
12.1
Projection Pursuit
241
12.2
Portfolio Optimization
243
viii Contents
12.3
Discriminant
and Cluster Analysis
244
12.4
Multiple Decision Problems
245
12.5
Other Applications
246
References
247
Index
269
Multivariate t
Distributions and Their Applications
Almost all of the results available in the literature on multivariate
t
distributions published in the last
50
years are now collected together in
this comprehensive volume. Because these distributions are becoming
more prominent in many applications, this book is a must for any serious
researcher or consultant working in multivariate analysis and statistical
distributions. Much of this material has never appeared in book form.
The first part of the book emphasizes theoretical results of a proba¬
bilistic nature. In the second part of the book, these are supplemented by
a variety of statistical aspects. Various generalizations and applications
are dealt with in the final chapters. The material on estimation and
regression models is of special value for practitioners in statistics and
economics. A comprehensive bibliography of more than
350
references is
included.
Samuel Kotz is Professor and Senior Research Scholar in the Depart¬
ment of Engineering Management and Systems Engineering at George
Washington University. In addition to holding many distinguished vis¬
iting positions at prominent universities, he has authored a number
of books and more than
100
articles, is Editor-in-Chief and founder
of the Encyclopedia of Statistical Sciences, and holds three honorary
doctorates.
Saralees Nadarajah is Professor of Mathematics at the University of
South Florida. He has made important contributions to distribution the¬
ory, extreme value theory and its applications in environmental model¬
ing, branching processes, and sampling theory. He has authored more
than
80
papers and two books.
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:39Z |
| institution | BVB |
| isbn | 0521826543 |
| language | English |
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| spelling | Kotz, Samuel 1930-2010 Verfasser (DE-588)119529653 aut Multivariate t-distributions and their applications Samuel Kotz ; Saralees Nadarajah 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2004 XII, 272 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Multivariate Wahrscheinlichkeitsverteilung (DE-588)4205373-0 gnd rswk-swf Multivariate Wahrscheinlichkeitsverteilung (DE-588)4205373-0 s DE-604 Nadarajah, Saralees Verfasser (DE-588)13585489X aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012790516&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012790516&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kotz, Samuel 1930-2010 Nadarajah, Saralees Multivariate t-distributions and their applications Multivariate Wahrscheinlichkeitsverteilung (DE-588)4205373-0 gnd |
| subject_GND | (DE-588)4205373-0 |
| title | Multivariate t-distributions and their applications |
| title_auth | Multivariate t-distributions and their applications |
| title_exact_search | Multivariate t-distributions and their applications |
| title_full | Multivariate t-distributions and their applications Samuel Kotz ; Saralees Nadarajah |
| title_fullStr | Multivariate t-distributions and their applications Samuel Kotz ; Saralees Nadarajah |
| title_full_unstemmed | Multivariate t-distributions and their applications Samuel Kotz ; Saralees Nadarajah |
| title_short | Multivariate t-distributions and their applications |
| title_sort | multivariate t distributions and their applications |
| topic | Multivariate Wahrscheinlichkeitsverteilung (DE-588)4205373-0 gnd |
| topic_facet | Multivariate Wahrscheinlichkeitsverteilung |
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