Holdings: Automatic nonuniform random variate generation

Automatic nonuniform random variate generation:

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Bibliographic Details
Main Authors:	Hörmann, Wolfgang (Author), Leydold, Josef (Author), Derflinger, Gerhard (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2004
Series:	Statistics and computing
Subjects:	Zufallsgenerator
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 441 S. graph. Darst.
ISBN:	3540406522

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MARC


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adam_text	CONTENTS PART I PRELIMINARIES 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 GENERAL PRINCIPLES IN RANDOM VARIATE GENERATION . . . . . . . . . 13 2.1 THE INVERSION METHOD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 THE REJECTION METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 COMPOSITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 THE RATIO-OF-UNIFORMS METHOD (ROU) . . . . . . . . . . . . . . . . . . . . . 32 2.5 ALMOST-EXACT INVERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 USING SPECIAL PROPERTIES OF THE DISTRIBUTION. . . . . . . . . . . . . . . . . 37 2.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3 GENERAL PRINCIPLES FOR DISCRETE DISTRIBUTIONS . . . . . . . . . . . . . . 43 3.1 INVERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 THE ALIAS METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3 DISCRETE REJECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.4 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 PART II CONTINUOUS UNIVARIATE DISTRIBUTIONS 4 TRANSFORMED DENSITY REJECTION (TDR) . . . . . . . . . . . . . . . . . . . . 55 4.1 THE MAIN IDEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 THE CLASS T C OF TRANSFORMATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 T C -CONCAVE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 CONSTRUCTION POINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.5 ALGORITHMS AND VARIANTS OF TRANSFORMED DENSITY REJECTION . . . 88 4.6 OTHER TRANSFORMATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.7 GENERALIZATIONS OF TRANSFORMED DENSITY REJECTION . . . . . . . . . . . 97 4.8 AUTOMATIC RATIO-OF-UNIFORMS METHOD . . . . . . . . . . . . . . . . . . . . . . 103 VIII CONTENTS 4.9 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5 STRIP METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.1 STAIRCASE-SHAPED HAT FUNCTIONS (AHRENS METHOD) . . . . . . . . . 114 5.2 HORIZONTAL STRIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.3 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6 METHODS BASED ON GENERAL INEQUALITIES . . . . . . . . . . . . . . . . . . . . 125 6.1 MONOTONE DENSITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.2 LIPSCHITZ DENSITIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.3 GENERATORS FOR T * 1 / 2 -CONCAVE DENSITIES . . . . . . . . . . . . . . . . . . . . 135 6.4 GENERATORS FOR T C -CONCAVE DENSITIES . . . . . . . . . . . . . . . . . . . . . . . 142 6.5 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7 NUMERICAL INVERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.1 SEARCH ALGORITHMS WITHOUT TABLES. . . . . . . . . . . . . . . . . . . . . . . . . 156 7.2 FAST NUMERICAL INVERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.3 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8 COMPARISON AND GENERAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . 165 8.1 THE UNU.RAN LIBRARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.2 TIMING RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.3 QUALITY OF GENERATED SAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 8.4 SPECIAL APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 8.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 9 DISTRIBUTIONS WHERE THE DENSITY IS NOT KNOWN EXPLICITLY . 193 9.1 KNOWN HAZARD-RATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.2 THE SERIES METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.3 KNOWN FOURIER COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 9.4 KNOWN CHARACTERISTIC FUNCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 9.5 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 PART III DISCRETE UNIVARIATE DISTRIBUTIONS 10 DISCRETE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 10.1 GUIDE TABLE METHOD FOR UNBOUNDED DOMAINS . . . . . . . . . . . . . . . 216 10.2 TRANSFORMED PROBABILITY REJECTION (TPR) . . . . . . . . . . . . . . . . . . 219 10.3 SHORT ALGORITHMS BASED ON GENERAL INEQUALITIES . . . . . . . . . . . . . 227 10.4 DISTRIBUTIONS WHERE THE PROBABILITIES ARE NOT KNOWN EXPLICITLY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 10.5 COMPUTATIONAL EXPERIENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 10.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 10.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 CONTENTS IX PART IV RANDOM VECTORS 11 MULTIVARIATE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 11.1 GENERAL PRINCIPLES FOR GENERATING RANDOM VECTORS . . . . . . . . . . 246 11.2 UNIFORMLY DISTRIBUTED RANDOM VECTORS . . . . . . . . . . . . . . . . . . . . 252 11.3 MULTIVARIATE TRANSFORMED DENSITY REJECTION . . . . . . . . . . . . . . . . 264 11.4 ORTHOMONOTONE DENSITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 11.5 COMPUTATIONAL EXPERIENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 11.6 MULTIVARIATE DISCRETE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . 295 11.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 PART V IMPLICIT MODELING 12 COMBINATION OF GENERATION AND MODELING . . . . . . . . . . . . . . . . . 305 12.1 GENERALIZING A SAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 12.2 GENERALIZING A VECTOR-SAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 12.3 MODELING OF DISTRIBUTIONS WITH LIMITED INFORMATION . . . . . . . . . 322 12.4 DISTRIBUTION WITH KNOWN MOMENTS . . . . . . . . . . . . . . . . . . . . . . . . 323 12.5 GENERATION OF RANDOM VECTORS WHERE ONLY CORRELATION AND MARGINAL DISTRIBUTIONS ARE KNOWN . . . . . . . . . . . . . . . . . . . . . . . . . 328 12.6 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13 TIME SERIES (AUTHORS MICHAEL HAUSER AND WOLFGANG H¨ ORMANN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 13.1 STATIONARY GAUSSIAN TIME SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . 347 13.2 NON-GAUSSIAN TIME SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 13.3 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 14 MARKOV CHAIN MONTE CARLO METHODS . . . . . . . . . . . . . . . . . . . . . . 363 14.1 MARKOV CHAIN SAMPLING ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . . 364 14.2 PERFECT SAMPLING FOR MARKOV CHAIN MONTE CARLO . . . . . . . . . . . . 372 14.3 MARKOV CHAIN MONTE CARLO METHODS FOR RANDOM VECTORS . . . . 376 14.4 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 15 SOME SIMULATION EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 15.1 FINANCIAL SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 15.2 BAYESIAN STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 15.3 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 LIST OF ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 AUTHOR INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 X CONTENTS SELECTED NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 SUBJECT INDEX AND GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
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spelling	Hörmann, Wolfgang Verfasser aut Automatic nonuniform random variate generation Wolfgang Hörmann ; Josef Leydold ; Gerhard Derflinger Berlin [u.a.] Springer 2004 X, 441 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Zufallsgenerator (DE-588)4191097-7 gnd rswk-swf Zufallsgenerator (DE-588)4191097-7 s DE-604 Leydold, Josef Verfasser aut Derflinger, Gerhard Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017436897&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hörmann, Wolfgang Leydold, Josef Derflinger, Gerhard Automatic nonuniform random variate generation Zufallsgenerator (DE-588)4191097-7 gnd
subject_GND	(DE-588)4191097-7
title	Automatic nonuniform random variate generation
title_auth	Automatic nonuniform random variate generation
title_exact_search	Automatic nonuniform random variate generation
title_full	Automatic nonuniform random variate generation Wolfgang Hörmann ; Josef Leydold ; Gerhard Derflinger
title_fullStr	Automatic nonuniform random variate generation Wolfgang Hörmann ; Josef Leydold ; Gerhard Derflinger
title_full_unstemmed	Automatic nonuniform random variate generation Wolfgang Hörmann ; Josef Leydold ; Gerhard Derflinger
title_short	Automatic nonuniform random variate generation
title_sort	automatic nonuniform random variate generation
topic	Zufallsgenerator (DE-588)4191097-7 gnd
topic_facet	Zufallsgenerator
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017436897&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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