Random number generation and Monte Carlo methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2003
|
| Edition: | 2. ed. |
| Series: | Statistics and computing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 381 S. Ill., graph. Darst. |
| ISBN: | 0387001786 |
Staff View
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| 100 | 1 | |a Gentle, James E. |d 1943- |e Verfasser |0 (DE-588)126727031 |4 aut | |
| 245 | 1 | 0 | |a Random number generation and Monte Carlo methods |c James E. Gentle |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2003 | |
| 300 | |a XV, 381 S. |b Ill., graph. Darst. | ||
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| 650 | 7 | |a Méthode de Monte-Carlo |2 rasuqam | |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PREFACE VII
1 SIMULATING RANDOM NUMBERS FROM A UNIFORM DISTRIBUTION 1 1.1 UNIFORM
INTEGERS AND AN APPROXIMATE UNIFORM DENSITY 5
1.2 SIMPLE LINEAR CONGRUENTIAL GENERATORS 11
1.2.1 STRUCTURE IN THE GENERATED NUMBERS 14
1.2.2 TESTS OF SIMPLE LINEAR CONGRUENTIAL GENERATORS 20
1.2.3 SHUFFLING THE OUTPUT STREAM 21
1.2.4 GENERATION OF SUBSTREAMS IN SIMPLE LINEAR CONGRUENTIAL GENERATORS
23
1.3 COMPUTER IMPLEMENTATION OF SIMPLE LINEAR CONGRUENTIAL GENERATORS 27
1.3.1 ENSURING EXACT COMPUTATIONS 28
1.3.2 RESTRICTION THAT THE OUTPUT BE IN THE OPEN INTERVAL (0,1) 29
1.3.3 EFFICIENCY CONSIDERATIONS 30
1.3.4 VECTOR PROCESSORS 30
1.4 OTHER LINEAR CONGRUENTIAL GENERATORS 31
1.4.1 MULTIPLE RECURSIVE GENERATORS 32
1.4.2 MATRIX CONGRUENTIAL GENERATORS 34
1.4.3 ADD-WITH-CARRY, SUBTRACT-WITH-BORROW, AND MULTIPLY-WITH-CARRY
GENERATORS 35
1.5 NONLINEAR CONGRUENTIAL GENERATORS 36
1.5.1 INVERSIVE CONGRUENTIAL GENERATORS 36
1.5.2 OTHER NONLINEAR CONGRUENTIAL GENERATORS 37
1.6 FEEDBACK SHIFT REGISTER GENERATORS 38
1.6.1 GENERALIZED FEEDBACK SHIFT REGISTERS AND VARIATIONS . .. 40 1.6.2
SKIPPING AHEAD IN GFSR GENERATORS 43
1.7 OTHER SOURCES OF UNIFORM RANDOM NUMBERS 43
1.7.1 GENERATORS BASED ON CELLULAR AUTOMATA 44
1.7.2 GENERATORS BASED ON CHAOTIC SYSTEMS 45
1.7.3 OTHER RECURSIVE GENERATORS 45
IMAGE 2
1.7.4 TABLES OF RANDOM NUMBERS 46
1.8 COMBINING GENERATORS 46
1.9 PROPERTIES OF COMBINED GENERATORS 48
1.10 INDEPENDENT STREAMS AND PARALLEL RANDOM NUMBER GENERATION . 51
1.10.1 SKIPPING AHEAD WITH COMBINATION GENERATORS 52 1.10.2 DIFFERENT
GENERATORS FOR DIFFERENT STREAMS 52 1.10.3 QUALITY OF PARALLEL RANDOM
NUMBER STREAMS 53 1.11 PORTABILITY OF RANDOM NUMBER GENERATORS 54
1.12 SUMMARY 55
EXERCISES 56
QUALITY OF RANDOM NUMBER GENERATORS 61
2.1 PROPERTIES OF RANDOM NUMBERS 62
2.2 MEASURES OF LACK OF FIT 64
2.2.1 MEASURES BASED ON THE LATTICE STRUCTURE 64
2.2.2 DIFFERENCES IN FREQUENCIES AND PROBABILITIES 67 2.2.3 INDEPENDENCE
70
2.3 EMPIRICAL ASSESSMENTS 71
2.3.1 STATISTICAL GOODNESS-OF-FIT TESTS 71
2.3.2 COMPARISONS OF SIMULATED RESULTS WITH STATISTICAL MODELS IN
PHYSICS 86
2.3.3 ANECDOTAL EVIDENCE 86
2.3.4 TESTS OF RANDOM NUMBER GENERATORS USED IN PARALLEL . . 87 2.4
PROGRAMMING ISSUES 87
2.5 SUMMARY 87
EXERCISES 88
QUASIRANDOM NUMBERS 93
3.1 LOW DISCREPANCY 93
3.2 TYPES OF SEQUENCES 94
3.2.1 HALTON SEQUENCES 94
3.2.2 SOBOL SEQUENCES 96
3.2.3 COMPARISONS 97
3.2.4 VARIATIONS 97
3.2.5 COMPUTATIONS 98
3.3 FURTHER COMMENTS 98
EXERCISES 100
TRANSFORMATIONS OF UNIFORM DEVIATES: GENERAL METHODS 101 4.1 INVERSE CDF
METHOD 102
4.2 DECOMPOSITIONS OF DISTRIBUTIONS 109
4.3 TRANSFORMATIONS THAT USE MORE THAN ONE UNIFORM DEVIATE . . . I LL
4.4 MULTIVARIATE UNIFORM DISTRIBUTIONS WITH NONUNIFORM MARGINALS . 112
4.5 ACCEPTANCE/REJECTION METHODS 113
4.6 MIXTURES AND ACCEPTANCE METHODS 125
IMAGE 3
4.7 RATIO-OF-UNIFORMS METHOD 129
4.8 ALIAS METHOD 133
4.9 USE OF THE CHARACTERISTIC FUNCTION 136
4.10 USE OF STATIONARY DISTRIBUTIONS OF MARKOV CHAINS 137
4.11 USE OF CONDITIONAL DISTRIBUTIONS 149
4.12 WEIGHTED RESAMPLING 149
4.13 METHODS FOR DISTRIBUTIONS WITH CERTAIN SPECIAL PROPERTIES . . ..
150 4.14 GENERAL METHODS FOR MULTIVARIATE DISTRIBUTIONS 155
4.15 GENERATING SAMPLES FROM A GIVEN DISTRIBUTION 159
EXERCISES 159
SIMULATING RANDOM NUMBERS FROM SPECIFIC DISTRIBUTIONS 165 5.1
MODIFICATIONS OF STANDARD DISTRIBUTIONS 167
5.2 SOME SPECIFIC UNIVARIATE DISTRIBUTIONS 170
5.2.1 NORMAL DISTRIBUTION 171
5.2.2 EXPONENTIAL, DOUBLE EXPONENTIAL, AND EXPONENTIAL POWER
DISTRIBUTIONS 176
5.2.3 GAMMA DISTRIBUTION 178
5.2.4 BETA DISTRIBUTION 183
5.2.5 CHI-SQUARED, STUDENT S T, AND F DISTRIBUTIONS 184 5.2.6 WEIBULL
DISTRIBUTION 186
5.2.7 BINOMIAL DISTRIBUTION 187
5.2.8 POISSON DISTRIBUTION 188
5.2.9 NEGATIVE BINOMIAL AND GEOMETRIC DISTRIBUTIONS 188 5.2.10
HYPERGEOMETRIC DISTRIBUTION 189
5.2.11 LOGARITHMIC DISTRIBUTION 190
5.2.12 OTHER SPECIFIC UNIVARIATE DISTRIBUTIONS 191
5.2.13 GENERAL FAMILIES OF UNIVARIATE DISTRIBUTIONS 193 5.3 SOME
SPECIFIC MULTIVARIATE DISTRIBUTIONS 197
5.3.1 MULTIVARIATE NORMAL DISTRIBUTION 197
5.3.2 MULTINOMIAL DISTRIBUTION 198
5.3.3 CORRELATION MATRICES AND VARIANCE-COVARIANCE MATRICES . 198 5.3.4
POINTS ON A SPHERE 201
5.3.5 TWO-WAY TABLES 202
5.3.6 OTHER SPECIFIC MULTIVARIATE DISTRIBUTIONS 203
5.3.7 FAMILIES OF MULTIVARIATE DISTRIBUTIONS 208
5.4 DATA-BASED RANDOM NUMBER GENERATION 210
5.5 GEOMETRIC OBJECTS 212
EXERCISES 213
GENERATION OF RANDOM SAMPLES, PERMUTATIONS, AND STOCHASTIC PROCESSES 217
6.1 RANDOM SAMPLES 217
6.2 PERMUTATIONS 220
6.3 LIMITATIONS OF RANDOM NUMBER GENERATORS 220
IMAGE 4
6.4 GENERATION OF NONINDEPENDENT SAMPLES 221
6.4.1 ORDER STATISTICS 221
6.4.2 CENSORED DATA 223
6.5 GENERATION OF NONINDEPENDENT SEQUENCES 224
6.5.1 MARKOV PROCESS 224
6.5.2 NONHOMOGENEOUS POISSON PROCESS 225
6.5.3 OTHER TIME SERIES MODELS 226
EXERCISES 227
MONTE CARLO METHODS 229
7.1 EVALUATING AN INTEGRAL 230
7.2 SEQUENTIAL MONTE CARLO METHODS 233
7.3 EXPERIMENTAL ERROR IN MONTE CARLO METHODS 235
7.4 VARIANCE OF MONTE CARLO ESTIMATORS 236
7.5 VARIANCE REDUCTION 239
7.5.1 ANALYTIC REDUCTION 240
7.5.2 STRATIFIED SAMPLING AND IMPORTANCE SAMPLING 241 7.5.3 USE OF
COVARIATES 245
7.5.4 CONSTRAINED SAMPLING 248
7.5.5 STRATIFICATION IN HIGHER DIMENSIONS: LATIN HYPERCUBE SAMPLING 248
7.6 THE DISTRIBUTION OF A SIMULATED STATISTIC 249
7.7 COMPUTATIONAL STATISTICS 250
7.7.1 MONTE CARLO METHODS FOR INFERENCE 251
7.7.2 BOOTSTRAP METHODS 252
7.7.3 EVALUATING A POSTERIOR DISTRIBUTION 255
7.8 COMPUTER EXPERIMENTS 256
7.9 COMPUTATIONAL PHYSICS 257
7.10 COMPUTATIONAL FINANCE 261
EXERCISES 271
SOFTWARE FOR RANDOM NUMBER GENERATION 283
8.1 THE USER INTERFACE FOR RANDOM NUMBER GENERATORS 285
8.2 CONTROLLING THE SEEDS IN MONTE CARLO STUDIES 286
8.3 RANDOM NUMBER GENERATION IN PROGRAMMING LANGUAGES . . .. 286 8.4
RANDOM NUMBER GENERATION IN IMSL LIBRARIES 288
8.5 RANDOM NUMBER GENERATION IN S-PLUS AND R 291
EXERCISES 295
MONTE CARLO STUDIES IN STATISTICS 297
9.1 SIMULATION AS AN EXPERIMENT 298
9.2 REPORTING SIMULATION EXPERIMENTS 300
9.3 AN EXAMPLE 301
EXERCISES 310
. NOTATION AND DEFINITIONS 313
IMAGE 5
B SOLUTIONS AND HINTS FOR SELECTED EXERCISES 323
BIBLIOGRAPHY 331
LITERATURE IN COMPUTATIONAL STATISTICS 332
WORLD WIDE WEB, NEWS GROUPS, LIST SERVERS, AND BULLETIN BOARDS . . 334
REFERENCES FOR SOFTWARE PACKAGES 336
REFERENCES TO THE LITERATURE 336
AUTHOR INDEX 371
SUBJECT INDEX 377
|
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| indexdate | 2024-07-09T19:18:04Z |
| institution | BVB |
| isbn | 0387001786 |
| language | English |
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| physical | XV, 381 S. Ill., graph. Darst. |
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| spelling | Gentle, James E. 1943- Verfasser (DE-588)126727031 aut Random number generation and Monte Carlo methods James E. Gentle 2. ed. New York [u.a.] Springer 2003 XV, 381 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Générateur de nombres aléatoires rasuqam Monte Carlo-methode gtt Méthode de Monte-Carlo rasuqam Willekeurige getallen gtt Monte Carlo method Random number generators Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Zufallsgenerator (DE-588)4191097-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s Zufallsgenerator (DE-588)4191097-7 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010509166&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gentle, James E. 1943- Random number generation and Monte Carlo methods Générateur de nombres aléatoires rasuqam Monte Carlo-methode gtt Méthode de Monte-Carlo rasuqam Willekeurige getallen gtt Monte Carlo method Random number generators Monte-Carlo-Simulation (DE-588)4240945-7 gnd Zufallsgenerator (DE-588)4191097-7 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4191097-7 |
| title | Random number generation and Monte Carlo methods |
| title_auth | Random number generation and Monte Carlo methods |
| title_exact_search | Random number generation and Monte Carlo methods |
| title_full | Random number generation and Monte Carlo methods James E. Gentle |
| title_fullStr | Random number generation and Monte Carlo methods James E. Gentle |
| title_full_unstemmed | Random number generation and Monte Carlo methods James E. Gentle |
| title_short | Random number generation and Monte Carlo methods |
| title_sort | random number generation and monte carlo methods |
| topic | Générateur de nombres aléatoires rasuqam Monte Carlo-methode gtt Méthode de Monte-Carlo rasuqam Willekeurige getallen gtt Monte Carlo method Random number generators Monte-Carlo-Simulation (DE-588)4240945-7 gnd Zufallsgenerator (DE-588)4191097-7 gnd |
| topic_facet | Générateur de nombres aléatoires Monte Carlo-methode Méthode de Monte-Carlo Willekeurige getallen Monte Carlo method Random number generators Monte-Carlo-Simulation Zufallsgenerator |
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| work_keys_str_mv | AT gentlejamese randomnumbergenerationandmontecarlomethods |