Principles of random variate generation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press [u.a.]
1988
|
| Series: | Oxford science publications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 228 Seiten |
| ISBN: | 0198522029 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Algorithmic conventions xiii
Glossary xvii
1 Simulation and random variate generation 1
1.1 The nature and origins of simulation 1
1.2 Simulation of dynamic, stochastic systems 4
1.3 Simulation in statistics 7
1.4 Simulation languages and new innovations 9
1.5 Random number and variate generation 10
1.5.1 Statistical reliability 11
1.5.2 Set up time 12
! 1.5.3 Marginal generation time 13
1.5.4 Portability/program length 14
1.5.5 Memory requirements 14
1.6 Further reading 14
2 Random number sequences 16
2.1 Introduction 16
2.2 Linear congruential generators 19
2.2.1 Mixed generators 20
2.2.2 Multiplicative generators 20
2.2.3 Theoretical tests of randomness 22
2.2.3.1 Mean, variance, and first order serial correlation 22
2.2.3.2 Potency 24
2.2.3.3 Lattice behaviour 26
2.3 Other types of generator 32
2.3.1 Fibonacci generators 32
2.3.2 Tauseworthe generators 33
2.3.3 Shuffled and portable generators 35
2.4 Empirical tests 37
2.4.1 Frequency test 37
2.4.2 Serial test 39
2.4.3 Gap test 40
2.4.4 Poker test 40
viii Contents
2.4.5 Coupon collector s test 42
2.4.6 The collision test 42
2.4.7 Runs test 43
2.4.8 Linear dependence 44
2.4.9 Concluding remarks 46
3 General methods for generating random
variates from univariate distributions 47
3.1 Inversion method 47
3.2 Composition method 50
3.3 Stochastic model methods 51
3.4 Envelope rejection 53
3.5 Band rejection 57
3.6 Ratio of uniforms method 60
3.7 Comparison of random numbers (Forsythe s method) 66
3.8 Alias rejection method 71
3.9 Polynomial sampling 74
3.10 Transformations involving multiple roots 76
3.10.1 Cauchy distribution 77
3.10.2 Standardized Wald distribution 78
3.11 Sampling from discrete empirical distributions 80
3.11.1 Sequential search 81
3.11.2 Ordered sequential search 83
3.11.3 Indexed search 84
3.11.4 Marsaglia s method 85
3.11.5 Method of Norman and Cannon 86
4 Methods of generation from specific
continuous distributions 89
4.1 Negative exponential 90
4.2 Normal distribution 93
4.2.1 Box Muller method 93
4.2.2 Butcher s method 95
4.2.3 Band rejection method 98
4.2.4 Ratio of uniforms method 99
4.2.5 Rectangle wedge tail method 101
4.2.6 The convenient and similar methods 103
4.2.7 Polynomial sampling and Forsythe s methods 105
4.2.8 Conclusions and recommendations 107
4.3 Gamma distribution 107
4.3.1 A ratio method (a 1) 108
4.3.2 Cauchy method (a ^ 1) 108
4.3.3 Log logistic method (a 0) 110
Contents ix
4.3.4 t distribution method (a 1) 111
4.3.5 Comparison of algorithms suitable for a ^ 1 113
4.3.6 A power transformation method (a 1) 115
4.3.7 A switching algorithm (a 1) 116
4.3.8 Beta method (a 1), and a comparison of methods 118
4.4 Beta distribution 120
4.4.1 Gamma method 120
4.4.2 Johnk s rejection method 121
4.4.3 Log logistic method 121
4.4.4 A family of switching algorithms 123
4.4.5 Comparison of methods 126
4.5 Chi squared, t, and / distributions 128
4.5.1 Chi squared distribution 128
4.5.2 t distribution 129
4.5.3 F distribution 131
4.6 Some other continuous distributions 132
4.6.1 Easily derived procedures 132
4.6.2 The generalized inverse Gaussian distribution 133
4.6.3 von Mises distribution 135
5 Discrete distributions 138
5.1 Poisson distribution 138
5.2 Binomial distribution 142
5.3 Negative binomial distribution 146
5.4 A family of alias algorithms for the binomial,
Poisson, and negative binomial distributions 148
5.5 Some monotonically decreasing probability mass functions 150
6 Multivariate distributions 155
6.1 Some general methods 155
6.1.1 Method of conditional distributions 155
6.1.2 Transformation to independent form 156
6.1.3 Rejection method 156
6.1.4 Stochastic model methods 156
6.2 Multivariate normal distribution 157
6.3 Wishart distribution 159
6.4 Bivariate exponential and Poisson distributions 161
6.4.1 A memoryless bivariate exponential distribution 161
6.4.2 Bivariate Poisson distribution 163
6.4.3 Other shock models leading to bivariate
and multivariate exponential distributions 165
6.5 Some other multivariate distributions 167
x Contents |
7 Miscellaneous topics 170
7.1 The generation of order statistics 170 .
7.1.1 Generation of uniform order statistics 170 I
7.1.2 Order statistics from general distributions 172
7.2 Simulation of stochastic processes 173
7.2.1 Heterogeneous Poisson process 173
7.2.2 Two dimensional Poisson process 177 j
7.2.3 Discrete state Markov processes 179
7.3 Sampling from distribution tails 184
7.3.1 Tail generation from the normal distribution 184
7.3.2 Tail generation from the gamma distribution 187
7.3.3 Tail generation from a f distribution 189
Appendix 1 FORTRAN 77 routines for generating
variates from selected distributions 191
1.1 RND (), random normal deviate 191
1.2 GAMMA(S), gamma calling routine 191
1.3 GAMMAl(S), gamma (S 1) 192
1.4 GAMMA2(S), gamma (S 1) 193
1.5 EXPON(), exponential 194
1.6 BETA(AA, BB), beta 194
1.7 TDISTN(M), Student s t 195
1.8 GIG(H, B), generalized inverse Gaussian 196
1.9 VMISES(SK), von Mises 197
1.10 IPOIS(E), Poisson calling routine 198
1.11 IPOISl(E), Poisson (E 20) 199
1.12 IPOIS2(E), Poisson [E 20) 199
1.13 IBINOM(PS, N), binomial 201
1.14 NBINOM(SK, P), negative binomial 202
1.15 MVNORM(N, H, D, F, FIRST, X), multivariate normal 203
Appendix 2 Graphical methods for sampling from
standardized gamma distributions (a ^ 1) and
the standardized normal distribution 205
2.1 Gamma (a = 1) 206
2.2 Gamma (a = 1.25) 207
2.3 Gamma (a = 1.5) 207
2.4 Gamma (a = 1.75) 208
2.5 Gamma (a = 2) 208
2.6 Gamma (a = 2.5) 209
2.7 Gamma (a = 3) 209
Contents xi
2.8 Gamma (a = 4) 210
2.9 Gamma (a = 5) 210
2.10 Gamma (a = 6) 211
2.11 Gamma (a = 7) 211
2.12 Gamma (a = 8) 212
2.13 Gamma (a = 9) 212
2.14 Gamma (a = 10) 213
2.15 Normal 213
References 214
Index 223
|
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| indexdate | 2024-07-09T15:26:58Z |
| institution | BVB |
| isbn | 0198522029 |
| language | English |
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| publishDate | 1988 |
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| spelling | Dagpunar, John Verfasser aut Principles of random variate generation John Dagpunar Oxford Clarendon Press [u.a.] 1988 XV, 228 Seiten txt rdacontent n rdamedia nc rdacarrier Oxford science publications Variables aléatoires Variables aléatoires ram Willekeurige variabelen gtt Random variables Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Stochastische Erzeugung (DE-588)4441717-2 gnd rswk-swf Zufallsgenerator (DE-588)4191097-7 gnd rswk-swf Zufallszahlen (DE-588)4124968-9 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 s DE-604 Zufallszahlen (DE-588)4124968-9 s Stochastische Erzeugung (DE-588)4441717-2 s Zufallsgenerator (DE-588)4191097-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000788347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dagpunar, John Principles of random variate generation Variables aléatoires Variables aléatoires ram Willekeurige variabelen gtt Random variables Zufallsvariable (DE-588)4129514-6 gnd Stochastische Erzeugung (DE-588)4441717-2 gnd Zufallsgenerator (DE-588)4191097-7 gnd Zufallszahlen (DE-588)4124968-9 gnd |
| subject_GND | (DE-588)4129514-6 (DE-588)4441717-2 (DE-588)4191097-7 (DE-588)4124968-9 |
| title | Principles of random variate generation |
| title_auth | Principles of random variate generation |
| title_exact_search | Principles of random variate generation |
| title_full | Principles of random variate generation John Dagpunar |
| title_fullStr | Principles of random variate generation John Dagpunar |
| title_full_unstemmed | Principles of random variate generation John Dagpunar |
| title_short | Principles of random variate generation |
| title_sort | principles of random variate generation |
| topic | Variables aléatoires Variables aléatoires ram Willekeurige variabelen gtt Random variables Zufallsvariable (DE-588)4129514-6 gnd Stochastische Erzeugung (DE-588)4441717-2 gnd Zufallsgenerator (DE-588)4191097-7 gnd Zufallszahlen (DE-588)4124968-9 gnd |
| topic_facet | Variables aléatoires Willekeurige variabelen Random variables Zufallsvariable Stochastische Erzeugung Zufallsgenerator Zufallszahlen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000788347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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