Simulation

by Ross

• ISBN13: 9780124158252
• ISBN10: 0124158250
• Edition: 5th
• Format: Hardcover
• Copyright: 2012-10-22
• Publisher: Elsevier Science

Summary

Ross's Simulation, Fifth Edition introduces aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers learn to apply results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions about future outcomes. This text explains how a computer can be used to generate random numbers, and how to use these random numbers to generate the behavior of a stochastic model over time. It presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model. 

Table of Contents

Preface	p. ix
Introduction	p. 1
Exercises	p. 3
Elements of Probability	p. 5
Sample Space and Events	p. 5
Axioms of Probability	p. 6
Conditional Probability and Independence	p. 7
Random Variables	p. 9
Expectation	p. 11
Variance	p. 14
Chebyshev's Inequality and the Laws of Large Numbers	p. 16
Some Discrete Random Variables	p. 18
Continuous Random Variables	p. 23
Conditional Expectation and Conditional Variance	p. 31
Exercises	p. 33
Bibliography	p. 38
Random Numbers	p. 39
Introduction	p. 39
Pseudorandom Number Generation	p. 39
Using Random Numbers to Evaluate Integrals	p. 40
Exercises	p. 44
Bibliography	p. 45
Generating Discrete Random Variables	p. 47
The Inverse Transform Method	p. 47
Generating a Poisson Random Variable	p. 54
Generating Binomial Random Variables	p. 55
The Acceptance-Rejection Technique	p. 56
The Composition Approach	p. 58
The Alias Method for Generating Discrete Random Variables	p. 60
Generating Random Vectors	p. 63
Exercises	p. 64
Generating Continuous Random Variables	p. 69
Introduction	p. 69
The Inverse Transform Algorithm	p. 69
The Rejection Method	p. 73
The Polar Method for Generating Normal Random Variables	p. 80
Generating a Poisson Process	p. 83
Generating a Nonhomogeneous Poisson Process	p. 85
Simulating a Two-Dimensional Poisson Process	p. 88
Exercises	p. 91
Bibliography	p. 95
The Multivariate Normal Distribution and Copulas	p. 97
Introduction	p. 97
The Multivariate Normal	p. 97
Generating a Multivariate Normal Random Vector	p. 99
Copulas	p. 102
Generating Variables from Copula Models	p. 107
Exercises	p. 108
The Discrete Event Simulation Approach	p. 111
Introduction	p. 111
Simulation via Discrete Events	p. 111
A Single-Server Queueing System	p. 112
A Queueing System with Two Servers in Series	p. 115
A Queueing System with Two Parallel Servers	p. 117
An Inventory Model	p. 120
An Insurance Risk Model	p. 122
A Repair Problem	p. 124
Exercising a Stock Option	p. 126
Verification of the Simulation Model	p. 128
Exercises	p. 129
Bibliography	p. 134
Statistical Analysis of Simulated Data	p. 135
Introduction	p. 135
The Sample Mean and Sample Variance	p. 135
Interval Estimates of a Population Mean	p. 141
The Bootstrapping Technique for Estimating Mean Square Errors	p. 144
Exercises	p. 150
Bibliography	p. 152
Variance Reduction Techniques	p. 153
Introduction	p. 153
The Use of Antithetic Variables	p. 155
The Use of Control Variates	p. 162
Variance Reduction by Conditioning	p. 169
Stratified Sampling	p. 182
Applications of Stratified Sampling	p. 192
Importance Sampling	p. 201
Using Common Random Numbers	p. 214
Evaluating an Exotic Option	p. 216
Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions	p. 220
Exercises	p. 222
Bibliography	p. 231
Additional Variance Reduction Techniques	p. 233
Introduction	p. 233
The Conditional Bernoulli Sampling Method	p. 233
Normalized Importance Sampling	p. 240
Latin Hypercube Sampling	p. 244
Exercises	p. 246
Statistical Validation Techniques	p. 247
Introduction	p. 247
Goodness of Fit Tests	p. 247
Goodness of Fit Tests When Some Parameters Are Unspecified	p. 254
The Two-Sample Problem	p. 257
Validating the Assumption of a Nonhomogeneous Poisson Process	p. 263
Exercises	p. 267
Bibliography	p. 270
Markov Chain Monte Carlo Methods	p. 271
Introduction	p. 271
Markov Chains	p. 271
The Hastings-Metropolis Algorithm	p. 274
The Gibbs Sampler	p. 276
Continuous time Markov Chains and a Queueing Loss Model	p. 287
Simulated Annealing	p. 290
The Sampling Importance Resampling Algorithm	p. 293
Coupling from the Past	p. 297
Exercises	p. 298
Bibliography	p. 301
Index	p. 303
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