Dirichlet and related distributions: theory, methods and applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2011
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Umschlagbild Inhaltsverzeichnis |
| Beschreibung: | XXVI, 310 S. graph. Darst. |
| ISBN: | 9780470688199 9781119995784 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV039641571 | ||
| 003 | DE-604 | ||
| 005 | 20121113 | ||
| 007 | t | ||
| 008 | 111017s2011 d||| |||| 00||| eng d | ||
| 020 | |a 9780470688199 |9 978-0-470-68819-9 | ||
| 020 | |a 9781119995784 |c oBook |9 978-1-119-99578-4 | ||
| 024 | 3 | |a 9780470688199 | |
| 035 | |a (OCoLC)729920658 | ||
| 035 | |a (DE-599)BVBBV039641571 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-634 |a DE-824 |a DE-20 |a DE-19 | ||
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 100 | 1 | |a Ng, Kai Wang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dirichlet and related distributions |b theory, methods and applications |c Kai Wang Ng ; Guo-Liang Tian ; Man-Lai Tang |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2011 | |
| 300 | |a XXVI, 310 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dirichlet-Problem |0 (DE-588)4129762-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |D s |
| 689 | 0 | 1 | |a Dirichlet-Problem |0 (DE-588)4129762-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tian, Guo-Liang |e Verfasser |4 aut | |
| 700 | 1 | |a Tang, Man-Lai |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-1-119-99841-9 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, MOBI |z 978-1-119-99842-6 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-1-119-99586-9 |
| 856 | 4 | 2 | |m V:DE-576;X:wiley |q application/pdf |u http://swbplus.bsz-bw.de/bsz343329247cov.htm |3 Umschlagbild |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024491471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024491471 | ||
Datensatz im Suchindex
| _version_ | 1804148496742219776 |
|---|---|
| adam_text | Titel: Dirichlet and related distributions
Autor: Ng, Kai W.
Jahr: 2011
Contents
Preface xiii
Acknowledgments xv
List of abbreviations xvii
List of symbols xix
List of figures xxiii
List of tables xxv
1 Introduction 1
1.1 Motivating examples 2
1.2 Stochastic representation and the = operator 7
1.2.1 Definition of stochastic representation 7
1.2.2 More properties on the = operator 11
1.3 Beta and inverted beta distributions 13
1.4 Some useful identities and integral formulae 16
1.4.1 Partial-fraction expansion 16
1.4.2 Cambanis-Keener-Simons integral formulae 16
1.4.3 Hermite-Genocchi integral formula 17
1.5 The Newton-Raphson algorithm 17
1.6 Likelihood in missing-data problems 18
1.6.1 Missing-data mechanism 18
1.6.2 The expectation-maximization (EM) algorithm 19
1.6.3 The expectation/conditional maximization (ECM) algorithm 22
1.6.4 The EM gradient algorithm 22
1.7 Bayesian MDPs and inversion of Bayes formula 23
1.7.1 The data augmentation (DA) algorithm 23
1.7.2 True nature of Bayesian MDP: inversion
of Bayes formula 25
1.7.3 Explicit solution to the DA integral equation 26
1.7.4 Sampling issues in Bayesian MDPs 29
1.8 Basic statistical distributions 30
1.8.1 Discrete distributions 30
1.8.2 Continuous distributions 32
viii CONTENTS
2 Dirichlet distribution 37
2.1 Definition and basic properties 38
2.1.1 Density function and moments 3 8
2.1.2 Stochastic representations and mode 40
2.2 Marginal and conditional distributions 43
2.3 Survival function and cumulative distribution function 45
2.3.1 Survival function 45
2.3.2 Cumulative distribution function 46
2.4 Characteristic functions 51
2.4.1 The characteristic function of u~ i/(T„ ) 51
2.4.2 The characteristic function of v ~ t/(V„) 53
2.4.3 The characteristic function of a Dirichlet random vector 55
2.5 Distribution for linear function of a Dirichlet random vector 57
2.5.1 Density for linear function of v ~ U(Yn ) 57
2.5.2 Density for linear function of u~ U(T„) 59
2.5.3 A unified approach to linear functions of variables
and order statistics 61
2.5.4 Cumulative distribution function for linear function
of a Dirichlet random vector 63
2.6 Characterizations 64
2.6.1 Mosimann s characterization 64
2.6.2 Darroch and Ratcliff s characterization 65
2.6.3 Characterization through neutrality 69
2.6.4 Characterization through complete neutrality 70
2.6.5 Characterization through global and local parameter
independence 72
2.7 MLEs of the Dirichlet parameters 72
2.7.1 MLE via the Newton-Raphson algorithm 72
2.7.2 MLE via the EM gradient algorithm 76
2.7.3 Analyzing serum-protein data of Pekin ducklings 76
2.8 Generalized method of moments estimation 77
2.8.1 Method of moments estimation 78
2.8.2 Generalized method of moments estimation 79
2.9 Estimation based on linear models 80
2.9.1 Preliminaries 81
2.9.2 Estimation based on individual linear models 84
2.9.3 Estimation based on the overall linear model 87
2.10 Application in estimating ROC area 92
2.10.1 The ROC curve 92
2.10.2 The ROC area 92
2.10.3 Computing the posterior density of the ROC area 94
2.10.4 Analyzing the mammogram data of breast cancer 95
3 Grouped Dirichlet distribution 97
3.1 Three motivating examples 98
3.2 Density function 99
CONTENTS ix
3.3 Basic properties 101
3.4 Marginal distributions 104
3.5 Conditional distributions 108
3.6 Extension to multiple partitions 110
3.6.1 Density function 110
3.6.2 Some properties 111
3.6.3 Marginal distributions 112
3.6.4 Conditional distributions 113
3.7 Statistical inferences: likelihood function with GDD form 115
3.7.1 Large-sample likelihood inference 116
3.7.2 Small-sample Bayesian inference 118
3.7.3 Analyzing the cervical cancer data 118
3.7.4 Analyzing the leprosy survey data 119
3.8 Statistical inferences: likelihood function beyond GDD form 121
3.8.1 Incomplete 2x2 contingency tables: the
neurological complication data 121
3.8.2 Incomplete r x c contingency tables 123
3.8.3 Wheeze study in six cities 132
3.8.4 Discussion 133
3.9 Applications under nonignorable missing data mechanism 134
3.9.1 Incomplete r x c tables: nonignorable missing mechanism 134
3.9.2 Analyzing the crime survey data 137
Nested Dirichlet distribution 141
4.1 Density function 142
4.2 Two motivating examples 142
4.3 Stochastic representation, mixed moments, and mode 144
4.4 Marginal distributions 148
4.5 Conditional distributions 150
4.6 Connection with exact null distribution for sphericity test 152
4.7 Large-sample likelihood inference 153
4.7.1 Likelihood with NDD form 154
4.7.2 Likelihood beyond NDD form 155
4.7.3 Comparison with existing likelihood strategies 156
4.8 Small-sample Bayesian inference 159
4.8.1 Likelihood with NDD form 159
4.8.2 Likelihood beyond NDD form 159
4.8.3 Comparison with the existing Bayesian strategy 160
4.9 Applications 162
4.9.1 Sample surveys with nonresponse: simulated data 162
4.9.2 Dental caries data 163
4.9.3 Competing-risks model: failure data for radio transmitter
receivers 166
4.9.4 Sample surveys: two data sets for death penalty attitude 169
4.9.5 Bayesian analysis of the ultrasound rating data 170
CONTENTS
4.10 A brief historical review 172
4.10.1 The neutrality principle 172
4.10.2 The short memory property 174
5 Inverted Dirichlet distribution 175
5.1 Definition through the density function 175
5.1.1 Density function 175
5.1.2 Several useful integral formulae 176
5.1.3 The mixed moment and the mode 177
5.2 Definition through stochastic representation 177
5.3 Marginal and conditional distributions 178
5.4 Cumulative distribution function and survival function 179
5.4.1 Cumulative distribution function 179
5.4.2 Survival function 182
5.5 Characteristic function 183
5.5.1 Univariate case 183
5.5.2 The confluent hypergeometric function of the second kind 183
5.5.3 General case 184
5.6 Distribution for linear function of inverted Dirichlet vector 185
5.6.1 Introduction 185
5.6.2 The distribution of the sum of independent gamma variâtes 186
5.6.3 The case of two dimensions 187
5.7 Connection with other multivariate distributions 188
5.7.1 Connection with the multivariate t distribution 188
5.7.2 Connection with the multivariate logistic distribution 190
5.7.3 Connection with the multivariate Pareto distribution 191
5.7.4 Connection with the multivariate Cook-Johnson
distribution 191
5.8 Applications 192
5.8.1 Bayesian analysis of variance in a linear model 192
5.8.2 Confidence regions for variance ratios in a linear
model with random effects 195
Dirichlet-multinomial distribution 199
6.1 Probability mass function 199
6.1.1 Motivation 199
6.1.2 Definition via a mixture representation 200
6.1.3 Beta-binomial distribution 201
6.2 Moments of the distribution 203
6.3 Marginal and conditional distributions 205
6.3.1 Marginal distributions 205
6.3.2 Conditional distributions 206
6.3.3 Multiple regression 207
CONTENTS xi
6.4 Conditional sampling method 207
6.5 The method of moments estimation 208
6.5.1 Observations and notations 208
6.5.2 The traditional moments method 209
6.5.3 Mosimann s moments method 210
6.6 The method of maximum likelihood estimation 212
6.6.1 The Newton-Raphson algorithm 212
6.6.2 The Fisher scoring algorithm 214
6.6.3 The EM gradient algorithm 216
6.7 Applications 218
6.7.1 The forest pollen data 218
6.7.2 The teratogenesis data 219
6.8 Testing the multinomial assumption against the
Dirichlet-multinomial alternative 221
6.8.1 The likelihood ratio statistic and its null distribution 221
6.8.2 The C(a) test 223
6.8.3 Two illustrative examples 225
7 Truncated Dirichlet distribution 227
7.1 Density function 227
7.1.1 Definition 227
7.1.2 Truncated beta distribution 228
7.2 Motivating examples 230
7.2.1 Case A: matrix Ë is known 231
7.2.2 Case B: matrix Ë is unknown 232
7.2.3 Case C: matrix Ë is partially known 232
7.3 Conditional sampling method 233
7.3.1 Consistent convex polyhedra 233
7.3.2 Marginal distributions 234
7.3.3 Conditional distributions 234
7.3.4 Generation of random vector from a truncated
Dirichlet distribution 236
7.4 Gibbs sampling method 237
7.5 The constrained maximum likelihood estimates 239
7.6 Application to misclassification 241
7.6.1 Screening test with binary misclassifications 241
7.6.2 Case-control matched-pair data with polytomous
misclassifications 242
7.7 Application to uniform design of experiment
with mixtures 245
8 Other related distributions 247
8.1 The generalized Dirichlet distribution 247
8.1.1 Density function 247
8.1.2 Statistical inferences 250
xii CONTENTS
8.1.3 Analyzing the crime survey data
8.1.4 Choice of an effective importance density
8.2 The hyper-Dirichlet distribution
8.2.1 Motivating examples
8.2.2 Density function
8.3 The scaled Dirichlet distribution
8.3.1 Two motivations
8.3.2 Stochastic representation and density function
8.3.3 Some properties
8.4 The mixed Dirichlet distribution
8.4.1 Density function
8.4.2 Stochastic representation
8.4.3 The moments
8.4.4 Marginal distributions
8.4.5 Conditional distributions
8.5 The Liouville distribution
8.6 The generalized Liouville distribution
Appendix A: Some useful S-plus Codes
References
Author index
Subject index
250
252
254
254
256
258
258
259
260
263
263
264
265
266
268
269
272
275
289
303
307
|
| any_adam_object | 1 |
| author | Ng, Kai Wang Tian, Guo-Liang Tang, Man-Lai |
| author_facet | Ng, Kai Wang Tian, Guo-Liang Tang, Man-Lai |
| author_role | aut aut aut |
| author_sort | Ng, Kai Wang |
| author_variant | k w n kw kwn g l t glt m l t mlt |
| building | Verbundindex |
| bvnumber | BV039641571 |
| classification_rvk | SK 800 |
| ctrlnum | (OCoLC)729920658 (DE-599)BVBBV039641571 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01969nam a2200457 c 4500</leader><controlfield tag="001">BV039641571</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20121113 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">111017s2011 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780470688199</subfield><subfield code="9">978-0-470-68819-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781119995784</subfield><subfield code="c">oBook</subfield><subfield code="9">978-1-119-99578-4</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9780470688199</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)729920658</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV039641571</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 800</subfield><subfield code="0">(DE-625)143256:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ng, Kai Wang</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dirichlet and related distributions</subfield><subfield code="b">theory, methods and applications</subfield><subfield code="c">Kai Wang Ng ; Guo-Liang Tian ; Man-Lai Tang</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Chichester</subfield><subfield code="b">Wiley</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXVI, 310 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Wiley series in probability and statistics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dirichlet-Problem</subfield><subfield code="0">(DE-588)4129762-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Dirichlet-Problem</subfield><subfield code="0">(DE-588)4129762-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tian, Guo-Liang</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tang, Man-Lai</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, EPUB</subfield><subfield code="z">978-1-119-99841-9</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, MOBI</subfield><subfield code="z">978-1-119-99842-6</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, PDF</subfield><subfield code="z">978-1-119-99586-9</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">V:DE-576;X:wiley</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://swbplus.bsz-bw.de/bsz343329247cov.htm</subfield><subfield code="3">Umschlagbild</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024491471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-024491471</subfield></datafield></record></collection> |
| id | DE-604.BV039641571 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:08:04Z |
| institution | BVB |
| isbn | 9780470688199 9781119995784 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024491471 |
| oclc_num | 729920658 |
| open_access_boolean | |
| owner | DE-634 DE-824 DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-634 DE-824 DE-20 DE-19 DE-BY-UBM |
| physical | XXVI, 310 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Ng, Kai Wang Verfasser aut Dirichlet and related distributions theory, methods and applications Kai Wang Ng ; Guo-Liang Tian ; Man-Lai Tang 1. publ. Chichester Wiley 2011 XXVI, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Dirichlet-Problem (DE-588)4129762-3 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Dirichlet-Problem (DE-588)4129762-3 s DE-604 Tian, Guo-Liang Verfasser aut Tang, Man-Lai Verfasser aut Erscheint auch als Online-Ausgabe, EPUB 978-1-119-99841-9 Erscheint auch als Online-Ausgabe, MOBI 978-1-119-99842-6 Erscheint auch als Online-Ausgabe, PDF 978-1-119-99586-9 V:DE-576;X:wiley application/pdf http://swbplus.bsz-bw.de/bsz343329247cov.htm Umschlagbild HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024491471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ng, Kai Wang Tian, Guo-Liang Tang, Man-Lai Dirichlet and related distributions theory, methods and applications Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Dirichlet-Problem (DE-588)4129762-3 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4129762-3 |
| title | Dirichlet and related distributions theory, methods and applications |
| title_auth | Dirichlet and related distributions theory, methods and applications |
| title_exact_search | Dirichlet and related distributions theory, methods and applications |
| title_full | Dirichlet and related distributions theory, methods and applications Kai Wang Ng ; Guo-Liang Tian ; Man-Lai Tang |
| title_fullStr | Dirichlet and related distributions theory, methods and applications Kai Wang Ng ; Guo-Liang Tian ; Man-Lai Tang |
| title_full_unstemmed | Dirichlet and related distributions theory, methods and applications Kai Wang Ng ; Guo-Liang Tian ; Man-Lai Tang |
| title_short | Dirichlet and related distributions |
| title_sort | dirichlet and related distributions theory methods and applications |
| title_sub | theory, methods and applications |
| topic | Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Dirichlet-Problem (DE-588)4129762-3 gnd |
| topic_facet | Wahrscheinlichkeitsverteilung Dirichlet-Problem |
| url | http://swbplus.bsz-bw.de/bsz343329247cov.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024491471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ngkaiwang dirichletandrelateddistributionstheorymethodsandapplications AT tianguoliang dirichletandrelateddistributionstheorymethodsandapplications AT tangmanlai dirichletandrelateddistributionstheorymethodsandapplications |