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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

Prefacep. ix
Introductionp. 1
Exercisesp. 3
Elements of Probabilityp. 5
Sample Space and Eventsp. 5
Axioms of Probabilityp. 6
Conditional Probability and Independencep. 7
Random Variablesp. 9
Expectationp. 11
Variancep. 14
Chebyshev's Inequality and the Laws of Large Numbersp. 16
Some Discrete Random Variablesp. 18
Continuous Random Variablesp. 23
Conditional Expectation and Conditional Variancep. 31
Exercisesp. 33
Bibliographyp. 38
Random Numbersp. 39
Introductionp. 39
Pseudorandom Number Generationp. 39
Using Random Numbers to Evaluate Integralsp. 40
Exercisesp. 44
Bibliographyp. 45
Generating Discrete Random Variablesp. 47
The Inverse Transform Methodp. 47
Generating a Poisson Random Variablep. 54
Generating Binomial Random Variablesp. 55
The Acceptance-Rejection Techniquep. 56
The Composition Approachp. 58
The Alias Method for Generating Discrete Random Variablesp. 60
Generating Random Vectorsp. 63
Exercisesp. 64
Generating Continuous Random Variablesp. 69
Introductionp. 69
The Inverse Transform Algorithmp. 69
The Rejection Methodp. 73
The Polar Method for Generating Normal Random Variablesp. 80
Generating a Poisson Processp. 83
Generating a Nonhomogeneous Poisson Processp. 85
Simulating a Two-Dimensional Poisson Processp. 88
Exercisesp. 91
Bibliographyp. 95
The Multivariate Normal Distribution and Copulasp. 97
Introductionp. 97
The Multivariate Normalp. 97
Generating a Multivariate Normal Random Vectorp. 99
Copulasp. 102
Generating Variables from Copula Modelsp. 107
Exercisesp. 108
The Discrete Event Simulation Approachp. 111
Introductionp. 111
Simulation via Discrete Eventsp. 111
A Single-Server Queueing Systemp. 112
A Queueing System with Two Servers in Seriesp. 115
A Queueing System with Two Parallel Serversp. 117
An Inventory Modelp. 120
An Insurance Risk Modelp. 122
A Repair Problemp. 124
Exercising a Stock Optionp. 126
Verification of the Simulation Modelp. 128
Exercisesp. 129
Bibliographyp. 134
Statistical Analysis of Simulated Datap. 135
Introductionp. 135
The Sample Mean and Sample Variancep. 135
Interval Estimates of a Population Meanp. 141
The Bootstrapping Technique for Estimating Mean Square Errorsp. 144
Exercisesp. 150
Bibliographyp. 152
Variance Reduction Techniquesp. 153
Introductionp. 153
The Use of Antithetic Variablesp. 155
The Use of Control Variatesp. 162
Variance Reduction by Conditioningp. 169
Stratified Samplingp. 182
Applications of Stratified Samplingp. 192
Importance Samplingp. 201
Using Common Random Numbersp. 214
Evaluating an Exotic Optionp. 216
Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functionsp. 220
Exercisesp. 222
Bibliographyp. 231
Additional Variance Reduction Techniquesp. 233
Introductionp. 233
The Conditional Bernoulli Sampling Methodp. 233
Normalized Importance Samplingp. 240
Latin Hypercube Samplingp. 244
Exercisesp. 246
Statistical Validation Techniquesp. 247
Introductionp. 247
Goodness of Fit Testsp. 247
Goodness of Fit Tests When Some Parameters Are Unspecifiedp. 254
The Two-Sample Problemp. 257
Validating the Assumption of a Nonhomogeneous Poisson Processp. 263
Exercisesp. 267
Bibliographyp. 270
Markov Chain Monte Carlo Methodsp. 271
Introductionp. 271
Markov Chainsp. 271
The Hastings-Metropolis Algorithmp. 274
The Gibbs Samplerp. 276
Continuous time Markov Chains and a Queueing Loss Modelp. 287
Simulated Annealingp. 290
The Sampling Importance Resampling Algorithmp. 293
Coupling from the Pastp. 297
Exercisesp. 298
Bibliographyp. 301
Indexp. 303
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