
Random Number Generation and Monte Carlo Methods
By:Â James E. Gentle
Hardcover | 14 September 2004 | Edition Number 2
At a Glance
404 Pages
Revised
23.5 x 15.88 x 1.91
Hardcover
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Industry Reviews
From the reviews of the second edition:
"The second edition covers advances since the first edition appeared in 1998, so this second edition I seven more valuable than the first. This edition, like the first, is aimed at the graduate level and would be useful for a course on random numbers." Technometrics, May 2004
"This book is an excellent reference for statisticians who need to generate pseudorandom numbers (PRN.) Gnelte brings together the literature in a helpful step-by-step format and provides copious references for those who want or need to dig deeper." Journal of Statsitical Software, April 2005
"The book gives an extensive introduction into the field of random number generation, theory and practice and shows some examples of their usage. ... contains a large bibliography, which is a valuable guide for further reading. The book is very useful for a practitioner ... . The book could also be used in a course on random number generation ... . All in all a book that people using Monte Carlo methods should have on their bookshelf." (dr. A. Hoogstrate, Kwantitatieve Methoden, Issue 72B24, 2004)
"I think this is a very good and useful book on the generation of random numbers and the use of Monte Carlo methods. It can be used as both, a reference and a textbook. It covers basic principles as well as newer methods such as parallel random number generation and Markov chain Monte Carlo. Also this book includes exercises which I find very use- and helpful in understanding this not so trivial field in computer mathematics." (Simulation News Europe (EUROSIM), Vol. 40, May, 2004)
"It has been stated and argued, to our minds convincingly, that 'the future of science will belong to...simulation-based modeling' ... . it is encouraging that Gentle devotes Chapters 1,2,3, and 8 ... to random number generation. ... Much of the rest of the book is concerned with generating variates from other distributions .... the future of science belongs to the modeler who educates him- or herself on uniform random number generators. This book is an excellent place to start that education." (Edward J. Dudewicz, Mary A. Owuor, SIAM Reviews, Vol. 47 (4), 2005)
"This book is a remarkable treatise on the theory and practice of random number generation. ... It allows the reader to understand the theoretical basis of each method and to implement it in a reliable manner. The writing is very precise but always easy to follow. Each chapter contains a host of theoretical and practical exercises. ... The completeness of the book make it an essential reference, but parts of it can also be used as a text book." (Ricardo Maronna, Statistical Papers, Vol. 47, 2005)
"This edition incorporates discussion of many advances in the field of random number generation and Monte Carlo methods since the appearance of the first edition of this book in 1998. ... There is a rather extensive list of references added at the end of the book. ... The book is intended to be both a reference and a textbook. It can be used as the primary text or as a supplementary text for a variety of courses at the graduate or advanced undergraduate level." (Volker Schmidt, Metrika, Vol. 64, 2006)
"The book may be most appropriately described as a handbook for random number generation. ... Each chapter has a set of exercises following it. The level of these make this book an ideal textbook for an undergraduate or introductory graduate course. ... Readers new to the field of randomization will find Gentle's book an excellent starting point for self study. A casual perusal of the book will be a good source of academic culture in this area of scientific pursuit." (Arnab Chakraborty, Sankhya, Vol. 65 (4), 2003)
| Preface | p. vii |
| Simulating Random Numbers from a Uniform Distribution | p. 1 |
| Uniform Integers and an Approximate Uniform Density | p. 5 |
| Simple Linear Congruential Generators | p. 11 |
| Structure in the Generated Numbers | p. 14 |
| Tests of Simple Linear Congruential Generators | p. 20 |
| Shuffling the Output Stream | p. 21 |
| Generation of Substreams in Simple Linear Congruential Generators | p. 23 |
| Computer Implementation of Simple Linear Congruential Generators | p. 27 |
| Ensuring Exact Computations | p. 28 |
| Restriction that the Output Be in the Open Interval (0,1) | p. 29 |
| Efficiency Considerations | p. 30 |
| Vector Processors | p. 30 |
| Other Linear Congruential Generators | p. 31 |
| Multiple Recursive Generators | p. 32 |
| Matrix Congruential Generators | p. 34 |
| Add-with-Carry, Subtract-with-Borrow, and Multiply-with-Carry Generators | p. 35 |
| Nonlinear Congruential Generators | p. 36 |
| Inversive Congruential Generators | p. 36 |
| Other Nonlinear Congruential Generators | p. 37 |
| Feedback Shift Register Generators | p. 38 |
| Generalized Feedback Shift Registers and Variations | p. 40 |
| Skipping Ahead in GFSR Generators | p. 43 |
| Other Sources of Uniform Random Numbers | p. 43 |
| Generators Based on Cellular Automata | p. 44 |
| Generators Based on Chaotic Systems | p. 45 |
| Other Recursive Generators | p. 45 |
| Tables of Random Numbers | p. 46 |
| Combining Generators | p. 46 |
| Properties of Combined Generators | p. 48 |
| Independent Streams and Parallel Random Number Generation | p. 51 |
| Skipping Ahead with Combination Generators | p. 52 |
| Different Generators for Different Streams | p. 52 |
| Quality of Parallel Random Number Streams | p. 53 |
| Portability of Random Number Generators | p. 54 |
| Summary | p. 55 |
| Exercises | p. 56 |
| Quality of Random Number Generators | p. 61 |
| Properties of Random Numbers | p. 62 |
| Measures of Lack of Fit | p. 64 |
| Measures Based on the Lattice Structure | p. 64 |
| Differences in Frequencies and Probabilities | p. 67 |
| Independence | p. 70 |
| Empirical Assessments | p. 71 |
| Statistical Goodness-of-Fit Tests | p. 71 |
| Comparisons of Simulated Results with Statistical Models in Physics | p. 86 |
| Anecdotal Evidence | p. 86 |
| Tests of Random Number Generators Used in Parallel | p. 87 |
| Programming Issues | p. 87 |
| Summary | p. 87 |
| Exercises | p. 88 |
| Quasirandom Numbers | p. 93 |
| Low Discrepancy | p. 93 |
| Types of Sequences | p. 94 |
| Halton Sequences | p. 94 |
| Sobol' Sequences | p. 96 |
| Comparisons | p. 97 |
| Variations | p. 97 |
| Computations | p. 98 |
| Further Comments | p. 98 |
| Exercises | p. 100 |
| Transformations of Uniform Deviates: General Methods | p. 101 |
| Inverse CDF Method | p. 102 |
| Decompositions of Distributions | p. 109 |
| Transformations that Use More than One Uniform Deviate | p. 111 |
| Multivariate Uniform Distributions with Nonuniform Marginals | p. 112 |
| Acceptance/Rejection Methods | p. 113 |
| Mixtures and Acceptance Methods | p. 125 |
| Ratio-of-Uniforms Method | p. 129 |
| Alias Method | p. 133 |
| Use of the Characteristic Function | p. 136 |
| Use of Stationary Distributions of Markov Chains | p. 137 |
| Use of Conditional Distributions | p. 149 |
| Weighted Resampling | p. 149 |
| Methods for Distributions with Certain Special Properties | p. 150 |
| General Methods for Multivariate Distributions | p. 155 |
| Generating Samples from a Given Distribution | p. 159 |
| Exercises | p. 159 |
| Simulating Random Numbers from Specific Distributions | p. 165 |
| Modifications of Standard Distributions | p. 167 |
| Some Specific Univariate Distributions | p. 170 |
| Normal Distribution | p. 171 |
| Exponential, Double Exponential, and Exponential Power Distributions | p. 176 |
| Gamma Distribution | p. 178 |
| Beta Distribution | p. 183 |
| Chi-Squared, Student's t, and F Distributions | p. 184 |
| Weibull Distribution | p. 186 |
| Binomial Distribution | p. 187 |
| Poisson Distribution | p. 188 |
| Negative Binomial and Geometric Distributions | p. 188 |
| Hypergeometric Distribution | p. 189 |
| Logarithmic Distribution | p. 190 |
| Other Specific Univariate Distributions | p. 191 |
| General Families of Univariate Distributions | p. 193 |
| Some Specific Multivariate Distributions | p. 197 |
| Multivariate Normal Distribution | p. 197 |
| Multinomial Distribution | p. 198 |
| Correlation Matrices and Variance-Covariance Matrices | p. 198 |
| Points on a Sphere | p. 201 |
| Two-Way Tables | p. 202 |
| Other Specific Multivariate Distributions | p. 203 |
| Families of Multivariate Distributions | p. 208 |
| Data-Based Random Number Generation | p. 210 |
| Geometric Objects | p. 212 |
| Exercises | p. 213 |
| Generation of Random Samples, Permutations, and Stochastic Processes | p. 217 |
| Random Samples | p. 217 |
| Permutations | p. 220 |
| Limitations of Random Number Generators | p. 220 |
| Generation of Nonindependent Samples | p. 221 |
| Order Statistics | p. 221 |
| Censored Data | p. 223 |
| Generation of Nonindependent Sequences | p. 224 |
| Markov Process | p. 224 |
| Nonhomogeneous Poisson Process | p. 225 |
| Other Time Series Models | p. 226 |
| Exercises | p. 227 |
| Monte Carlo Methods | p. 229 |
| Evaluating an Integral | p. 230 |
| Sequential Monte Carlo Methods | p. 233 |
| Experimental Error in Monte Carlo Methods | p. 235 |
| Variance of Monte Carlo Estimators | p. 236 |
| Variance Reduction | p. 239 |
| Analytic Reduction | p. 240 |
| Stratified Sampling and Importance Sampling | p. 241 |
| Use of Covariates | p. 245 |
| Constrained Sampling | p. 248 |
| Stratification in Higher Dimensions: Latin Hypercube Sampling | p. 248 |
| The Distribution of a Simulated Statistic | p. 249 |
| Computational Statistics | p. 250 |
| Monte Carlo Methods for Inference | p. 251 |
| Bootstrap Methods | p. 252 |
| Evaluating a Posterior Distribution | p. 255 |
| Computer Experiments | p. 256 |
| Computational Physics | p. 257 |
| Computational Finance | p. 261 |
| Exercises | p. 271 |
| Software for Random Number Generation | p. 283 |
| The User Interface for Random Number Generators | p. 285 |
| Controlling the Seeds in Monte Carlo Studies | p. 286 |
| Random Number Generation in Programming Languages | p. 286 |
| Random Number Generation in IMSL Libraries | p. 288 |
| Random Number Generation in S-Plus and R | p. 291 |
| Exercises | p. 295 |
| Monte Carlo Studies in Statistics | p. 297 |
| Simulation as an Experiment | p. 298 |
| Reporting Simulation Experiments | p. 300 |
| An Example | p. 301 |
| Exercises | p. 310 |
| Notation and Definitions | p. 313 |
| Solutions and Hints for Selected Exercises | p. 323 |
| Bibliography | p. 331 |
| Literature in Computational Statistics | p. 332 |
| World Wide Web, News Groups, List Servers, and Bulletin Boards | p. 334 |
| References for Software Packages | p. 336 |
| References to the Literature | p. 336 |
| Author Index | p. 371 |
| Subject Index | p. 377 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9780387001784
ISBN-10: 0387001786
Series: Statistics and Computing
Published: 14th September 2004
Format: Hardcover
Language: English
Number of Pages: 404
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Edition Number: 2
Edition Type: Revised
Dimensions (cm): 23.5 x 15.88 x 1.91
Weight (kg): 0.69
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