Random number generation and Monte Carlo methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2005
|
| Ausgabe: | 2. ed., corr. 2. print |
| Schriftenreihe: | Statistics and computing
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 381 S. Ill., graph. Darst. |
| ISBN: | 0387001786 |
Internformat
MARC
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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., corr. 2. print | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2005 | |
| 300 | |a XV, 381 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics and computing | |
| 650 | 4 | |a Monte-Carlo-Simulation - Zufallsgenerator | |
| 650 | 4 | |a Monte Carlo method | |
| 650 | 4 | |a Random number generators | |
| 650 | 0 | 7 | |a Zufallsgenerator |0 (DE-588)4191097-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |D s |
| 689 | 0 | 1 | |a Zufallsgenerator |0 (DE-588)4191097-7 |D s |
| 689 | 0 | |5 DE-188 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014909274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014909274 | ||
Datensatz im Suchindex
| _version_ | 1804135523448520704 |
|---|---|
| adam_text | 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
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
. . .111
4.4
Multivariate Uniform Distributions with
Nonuniform
Marginals
. 112
4.5
Acceptance/Rejection Methods
................... 113
4.6
Mixtures and Acceptance Methods
.................125
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
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
7
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
8
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
9
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
A Notation and Definitions
313
В
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
|
| adam_txt |
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
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
. . .111
4.4
Multivariate Uniform Distributions with
Nonuniform
Marginals
. 112
4.5
Acceptance/Rejection Methods
. 113
4.6
Mixtures and Acceptance Methods
.125
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
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
7
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
8
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
9
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
A Notation and Definitions
313
В
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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Gentle, James E. 1943- |
| author_GND | (DE-588)126727031 |
| author_facet | Gentle, James E. 1943- |
| author_role | aut |
| author_sort | Gentle, James E. 1943- |
| author_variant | j e g je jeg |
| building | Verbundindex |
| bvnumber | BV021695257 |
| classification_rvk | QH 239 SK 820 SK 830 SK 900 |
| classification_tum | MAT 107f MAT 629f MAT 639f |
| ctrlnum | (OCoLC)474685383 (DE-599)BVBBV021695257 |
| dewey-full | 519.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.282 |
| dewey-search | 519.282 |
| dewey-sort | 3519.282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., corr. 2. print |
| format | Book |
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| id | DE-604.BV021695257 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:15:37Z |
| indexdate | 2024-07-09T20:41:51Z |
| institution | BVB |
| isbn | 0387001786 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014909274 |
| oclc_num | 474685383 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-29T DE-11 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-29T DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | XV, 381 S. Ill., graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics and computing |
| spelling | Gentle, James E. 1943- Verfasser (DE-588)126727031 aut Random number generation and Monte Carlo methods James E. Gentle 2. ed., corr. 2. print New York [u.a.] Springer 2005 XV, 381 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Monte-Carlo-Simulation - Zufallsgenerator Monte Carlo method Random number generators Zufallsgenerator (DE-588)4191097-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s Zufallsgenerator (DE-588)4191097-7 s DE-188 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014909274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gentle, James E. 1943- Random number generation and Monte Carlo methods Monte-Carlo-Simulation - Zufallsgenerator Monte Carlo method Random number generators Zufallsgenerator (DE-588)4191097-7 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4191097-7 (DE-588)4240945-7 |
| 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_exact_search_txtP | 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 | Monte-Carlo-Simulation - Zufallsgenerator Monte Carlo method Random number generators Zufallsgenerator (DE-588)4191097-7 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Monte-Carlo-Simulation - Zufallsgenerator Monte Carlo method Random number generators Zufallsgenerator Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014909274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gentlejamese randomnumbergenerationandmontecarlomethods |