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WILEY-INTERSCIENCE PAPERBACK SERIES

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

". . .this is a very competently written and useful addition to the statistical literature; a book every statistician should look at and that many should study!"
—Short Book Reviews, International Statistical Institute

". . .reading this book was an enjoyable learning experience. The suggestions and recommendations on the methods [make] this book an excellent reference for anyone interested in simulation. With its compact structure and good coverage of material, it [is] an excellent textbook for a simulation course."
—Technometrics

". . .this work is an excellent comprehensive guide to simulation methods, written by a very competent author. It is especially recommended for those users of simulation methods who want more than a 'cook book'. "
—Mathematics Abstracts

This book is a comprehensive guide to simulation methods with explicit recommendations of methods and algorithms. It covers both the technical aspects of the subject, such as the generation of random numbers, non-uniform random variates and stochastic processes, and the use of simulation. Supported by the relevant mathematical theory, the text contains a great deal of unpublished research material, including coverage of the analysis of shift-register generators, sensitivity analysis of normal variate generators, analysis of simulation output, and more.

New feature

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

". . .this is a very competently written and useful addition to the statistical literature; a book every statistician should look at and that many should study!"
—Short Book Reviews, International Statistical Institute

". . .reading this book was an enjoyable learning experience. The suggestions and recommendations on the methods [make] this book an excellent reference for anyone interested in simulation. With its compact structure and good coverage of material, it [is] an excellent textbook for a simulation course."
—Technometrics

". . .this work is an excellent comprehensive guide to simulation methods, written by a very competent author. It is especially recommended for those users of simulation methods who want more than a 'cook book'. "
—Mathematics Abstracts

This book is a comprehensive guide to simulation methods with explicit recommendations of methods and algorithms. It covers both the technical aspects of the subject, such as the generation of random numbers, non-uniform random variates and stochastic processes, and the use of simulation. Supported by the relevant mathematical theory, the text contains a great deal of unpublished research material, including coverage of the analysis of shift-register generators, sensitivity analysis of normal variate generators, analysis of simulation output, and more.

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CONTENTS
1. Aims of Simulation = 1
 1.1. The Tools = 2
 1.2. Models = 2
 1.3. Simulation as Experimentation = 4
 1.4. Simulation in Inference = 4
 1.5. Examples = 5
 1.6. Literature = 12
 1.7. Convention = 12
 Exercises = 13
2. Pseudo-Random Numbers = 14
 2.1. History and Philosophy = 14
 2.2. Congruential Generators = 20
 2.3. Shift-Register Generators = 26
 2.4. Lattice Structure = 33
 2.5. Shuffling and Testing = 42
 2.6. Conclusions = 45
 2.7. Proofs = 46
 Exercises = 50
3. Random Variables = 53
 3.1. Simple Examples = 54
 3.2. General Principles = 59
 3.3. Discrete Distributions = 71
 3.4. Continuous Distributions = 81
 3.5. Recommendations = 91
 Exercises = 92
4. Stochasitc Models = 96
 4.1. Order Statistics = 96
 4.2. Multivariate Distribution = 98
 4.3. Poisson Processes and Lifetimes = 100
 4.4. Markov Processes = 104
 4.5. Gaussian Processes = 105
 4.6. Point Processes = 110
 4.7. Metropolis' Method and Random Fields = 113
 Exercises = 116
5. Variance Reduction = 118
 5.1. Monte-Carlo Integration = 119
 5.2. Importance Sampling = 122
 5.3. Control and Antithetic Variates = 123
 5.4. Conditioning = 134
 5.5. Experimental Design = 137
 Exercises = 139
6. Output Analysis = 142
 6.1. The Initial Transient = 146
 6.2. Batching = 150
 6.3. Time-Series Methods = 155
 6.4. Regenerative Simulation = 157
 6.5. A Case Study = 161
 Exercises = 169
7. Uses of Simulation = 170
 7.1. Statistical Inference = 171
 7.2. Stochastic Methods in Optimization = 178
 7.3. Systems of Linear Equations = 186
 7.4. Quasi-Monte-Carlo Integration = 189
 7.5. Sharpening Buffon's Needle = 193
 Exercises = 198
References = 200
Appendix A. Computer Systems = 215
Appendix B. Computer Programs = 217
 B.1. Form a × b mod c = 217
 B.2. Check Primitive Roots = 219
 B.3. Lattice Constants for Congruential Generators = 220
 B.4. Test GFSR Generators = 227
 B.5. Normal Variates = 228
 B.6. Exponential Variates = 230
 B.7. Gamma Variates = 230
 B.8. Discrete Distribution = 231
Index = 235