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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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