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. |