| 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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
