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Random Number Generation and Monte Carlo Methods [Kõva köide]

(George Mason University, Fairfax, Virginia, USA)
  • Formaat: Hardback, 240 pages, Illustrations
  • Sari: Statistics and Computing
  • Ilmumisaeg: 01-Sep-1998
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387985220
  • ISBN-13: 9780387985220
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Random Number Generation and Monte Carlo MethodsSuurem pilt
  • Formaat: Hardback, 240 pages, Illustrations
  • Sari: Statistics and Computing
  • Ilmumisaeg: 01-Sep-1998
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387985220
  • ISBN-13: 9780387985220
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780387985220.html
Märksõnad:
This text surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. It covers basic principles, as well as methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. Methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in late-1990s computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computations statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners.
Preface vii
1 Simulating Random Numbers from a Uniform Distribution
1(40)
1.1 Linear Congruential Generators
6(13)
1.1.1 Structure in the Generated Numbers
8(6)
1.1.2 Skipping Ahead in Linear Congruential Generators
14(2)
1.1.3 Shuffling the Output Stream
16(1)
1.1.4 Tests of Linear Congruential Generators
17(2)
1.2 Computer Implementation of Linear Congruential Generators
19(3)
1.2.1 Insuring Exact Computations
19(1)
1.2.2 Restriction that the Output Be Greater than 0 and Less than 1
20(1)
1.2.3 Efficiency Considerations
21(1)
1.2.4 Vector Processors
21(1)
1.3 Other Congruential Generators
22(4)
1.3.1 Multiple Recursive Generators
22(1)
1.3.2 Lagged Fibonacci
23(1)
1.3.3 Add-with-Carry, Subtract-with-Borrow, and Multiply-with-Carry Generators
23(1)
1.3.4 Inversive Congruential Generators
24(1)
1.3.5 Other Nonlinear Congruential Generators
25(1)
1.3.6 Matrix Congruential Generators
26(1)
1.4 Feedback Shift Register Generators
26(4)
1.4.1 Generalized Feedback Shift Registers and Variations
28(2)
1.4.2 Skipping Ahead in GFSR Generators
30(1)
1.5 Other Sources of Uniform Random Numbers
30(1)
1.5.1 Generators Based on Chaotic Systems
31(1)
1.5.2 Tables of Random Numbers
31(1)
1.6 Portable Random Number Generators
31(1)
1.7 Combining Generators
32(4)
1.7.1 Wichmann/Hill Generator
33(1)
1.7.2 L'Ecuyer Combined Generators
33(1)
1.7.3 Properties of Combined Generators
34(2)
1.8 Independent Streams and Parallel Random Number Generation
36(2)
1.8.1 Lehmer Trees
36(1)
1.8.2 Combination Generators
37(1)
1.8.3 Monte Carlo on Parallel Processors
37(1)
Exercises
38(3)
2 Transformations of Uniform Deviates: General Methods
41(44)
2.1 Inverse CDF Method
42(5)
2.2 Acceptance/Rejection Methods
47(8)
2.3 Mixtures of Distributions
55(2)
2.4 Mixtures and Acceptance Methods
57(2)
2.5 Ratio-of-Uniforms Method
59(2)
2.6 Alias Method
61(2)
2.7 Use of Stationary Distributions of Markov Chains
63(9)
2.8 Weighted Resampling
72(1)
2.9 Methods for Distributions with Certain Special Properties
72(4)
2.10 General Methods for Multivariate Distributions
76(4)
2.11 Generating Samples from a Given Distribution
80(1)
Exercises
80(5)
3 Simulating Random Numbers from Specific Distributions
85(36)
3.1 Some Specific Univariate Distributions
87(18)
3.1.1 Standard Distributions and Floded Distributions
87(1)
3.1.2 Normal Distribution
88(4)
3.1.3 Exponential, Double Exponential, and Exponential Power Distributions
92(1)
3.1.4 Gamma Distribution
93(3)
3.1.5 Beta Distribution
96(1)
3.1.6 Student's t, Chi-Squared, and F Distributions
97(2)
3.1.7 Weibull Distribution
99(1)
3.1.8 Binomial Distribution
99(1)
3.1.9 Poisson Distribution
100(1)
3.1.10 Negative Binomial and Geometric Distributions
101(1)
3.1.11 Hypergeometric Distribution
101(1)
3.1.12 Logarithmic Distribution
102(1)
3.1.13 Other Specific Univariate Distributions
102(2)
3.1.14 General Families of Univariate Distributions
104(1)
3.2 Some Specific Multivariate Distributions
105(7)
3.2.1 Multivariate Normal Distribution
105(1)
3.2.2 Multinomial Distribution
106(1)
3.2.3 Correlation Matrices and Variance-Covariance Matrices
107(2)
3.2.4 Points on a Sphere
109(1)
3.2.5 Two-Way Tables
110(1)
3.2.6 Other Specific Multivariate Distributions
111(1)
3.3 General Multivariate Distributions
112(5)
3.3.1 Distributions with Specified Correlations
112(3)
3.3.2 Data-Based Random Number Generation
115(2)
3.4 Geometric Objects
117(1)
Exercises
118(3)
4 Generation of Random Samples and Permutations
121(10)
4.1 Random Samples
121(2)
4.2 Permutations
123(1)
4.3 Generation of Nonindependent Samples
124(4)
4.3.1 Order Statistics
125(1)
4.3.2 Nonindependent Sequences: Nonhomogeneous Poisson Process
126(1)
4.3.3 Censored Data
127(1)
Exercises
128(3)
5 Monte Carlo Methods
131(20)
5.1 Evaluating an Integral
131(2)
5.2 Variance of Monte Carlo Estimators
133(2)
5.3 Variance Reduction
135(5)
5.3.1 Analytic Reduction
135(1)
5.3.2 Antithetic Variates
136(1)
5.3.3 Importance and Stratified Sampling
137(1)
5.3.4 Common Variates
137(1)
5.3.5 Constrained Sampling
138(1)
5.3.6 Latin Hypercube Sampling
138(2)
5.4 Computer Experiments
140(1)
5.5 Computational Statistics
141(4)
5.5.1 Monte Carlo Methods for Inference
141(1)
5.5.2 Bootstrap Methods
142(3)
5.6 Evaluating a Posterior Distribution
145(1)
Exercises
146(5)
6 Quality of Random Number Generators
151(16)
6.1 Analysis of the Algorithm
151(3)
6.2 Empirical Assessments
154(5)
6.2.1 Statistical Tests
154(4)
6.2.2 Anecdotal Evidence
158(1)
6.3 Quasirandom Numbers
159(5)
6.3.1 Halton Sequences
160(1)
6.3.2 Sobol' Sequences
161(1)
6.3.3 Comparisons
162(1)
6.3.4 Variations
163(1)
6.3.5 Some Examples of Applications
163(1)
6.3.6 Computations
164(1)
6.4 Programming Issues
164(1)
Exercises
164(3)
7 Software for Random Number Generation
167(10)
7.1 The User Interface for Random Number Generators
168(1)
7.2 Controlling the Seeds in Monte Carlo Studies
169(1)
7.3 Random Number Generation in IMSL Libraries
169(3)
7.4 Random Number Generation in S-Plus
172(2)
Exercises
174(3)
8 Monte Carlo Studies in Statistics
177(16)
8.1 Simulation as an Experiment
178(2)
8.2 Reporting Simulation Experiments
180(1)
8.3 An Example
180(10)
Exercises
190(3)
A Notation and Definitions
193(6)
B Solutions and Hints for Selected Exercises
199(6)
Bibliography 205(32)
Literature in Computational Statistics 206(2)
World Wide Web, News Groups, List Servers, and Bulletin Boards 208(3)
References 211(26)
Author Index 237(6)
Subject Index 243