Preface
1 Introduction
Exercises
2 Elements of Probability
2.1 Sample Space and Events
2.2 Axioms of Probability
2.3 Conditional Probability and Independence
2.4 Random Variables
2.5 Expectation
2.6 Variance
2.7 Chebyshev's Inequality and the Laws of Large Numbers
2.8 Some Discrete Random Variables
2.9 Continuous Random Variables
2.10 Conditional Expectation and Conditional Variance
Exercises
Bibliography
3 Random Numbers
Introduction
3.1 Pseudorandom Number Generation
3.2 Using Random Numbers to Evaluate Integrals
Exercises
Bibliography
4 Generating Discrete Random Variables
4.1 The Inverse Transform Method
4.2 Generating a Poisson Random Variable
4.3 Generating Binomial Random Variables
4.4 The Acceptance-Rejection Technique
4.5 The Composition Approach
4.6 The Alias Method for Generating Discrete Random
Variables
4.7 Generating Random Vectors
Exercises
5 Generating Continuous Random Variables
Introduction
5.1 The Inverse Transform Algorithm
5.2 The Rejection Method
5.3 The Polar Method for Generating Normal Random
Variables
5.4 Generating a Poisson Process
5.5 Generating a Nonhomogeneous Poisson Process
5.6 Simulating a Two-Dimensional Poisson Process
Exercises
Bibliography
6 The Multivariate Normal Distributiori and COPulas
Introduction
6.1 The Multivariate Normal
6.2 Generating a Multivariate Normal Random Vector
6.3 Copulas
6.4 Generating Variables from Copula Models
Exercises
7 The Discrete Event Simulation Approach
Introduction
7.1 Simulation via Discrete Events
7.2 A Single-Server Queueing System
7.3 A Queueing System with Two Servers in Series
7.4 A Queueing System with Two Parallel Servers
7.5 An Inventory Model
7.6 An Insurance Risk Model
7.7 A Repair Problem
7.8 Exercising a Stock Option
……
8 Statistical Analysis of Simulated Data
9 Variance Reduction Techniques
10 AdditionaIVoriance Reduction Techniques
11 Statistical Validation Techniques
12 Markov Chain Monte Carlo Methods
Index
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