The 5^th edition of Ross’s Simulation continues to introduce 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 latest edition features all-new material on variance reduction, including control variables and their use in estimating the expected return at blackjack and their relation to regression analysis. Additionally, the 5^th edition expands on Markov chain monte carlo methods, and offers unique information on the alias method for generating discrete random variables.

By explaining 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, Ross’s Simulation, 5^th edition presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.

Reviews

"I have always liked Ross’ books, as he is simultaneously mathematically rigorous and very interested in applications. The biggest strength I see is the rare combination of mathematical rigor and illustration of how the mathematical methodologies are applied in practice. Books with practical perspective are rarely this rigourous and mathematically detailed. I also like the variety of exercises, which are quite challenging and demanding excellence from students." --Prof. Krzysztof Ostaszewski, Illinois State University

Feature

• Additional material on variance reduction, including control variables and their use in estimating the expected return at blackjack and their relation to regression analysis
• Additional material and examples on Markov chain Monte Carlo methods
• Unique material on the alias method for generating discrete random variables
• Additional material on generating multivariate normal vectors

Preface Overview New to This Edition Chapter Descriptions Thanks Chapter 1. Introduction Exercises Chapter 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 References Chapter 3. Random Numbers Introduction 3.1 Pseudorandom Number Generation 3.2 Using Random Numbers to Evaluate Integrals Exercises References Chapter 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 Chapter 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 References Chapter 6. The Multivariate Normal Distribution 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 Chapter 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 7.9 Verification of the Simulation Model Exercises References Chapter 8. Statistical Analysis of Simulated Data Introduction 8.1 The Sample Mean and Sample Variance 8.2 Interval Estimates of a Population Mean 8.3 The Bootstrapping Technique for Estimating Mean Square Errors Exercises References Chapter 9. Variance Reduction Techniques Introduction 9.1 The Use of Antithetic Variables 9.2 The Use of Control Variates 9.3 Variance Reduction by Conditioning 9.4 Stratified Sampling 9.5 Applications of Stratified Sampling 9.6 Importance Sampling 9.7 Using Common Random Numbers 9.8 Evaluating an Exotic Option 9.9 Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions Exercises References Chapter 10. Additional Variance Reduction Techniques Introduction 2 The Conditional Bernoulli Sampling Method 3 Normalized Importance Sampling 4 Latin Hypercube Sampling Exercises Chapter 11. Statistical Validation Techniques Introduction 11.1 Goodness of Fit Tests 11.2 Goodness of Fit Tests When Some Parameters Are Unspecified 11.3 The Two-Sample Problem 11.4 Validating the Assumption of a Nonhomogeneous Poisson Process Exercises References Chapter 12. Markov Chain Monte Carlo Methods Introduction 12.1 Markov Chains 12.2 The Hastings–Metropolis Algorithm 12.3 The Gibbs Sampler 12.4 Continuous time Markov Chains and a QueueingLoss Model 12.5 Simulated Annealing 12.6 The Sampling Importance Resampling Algorithm 12.7 Coupling from the Past Exercises References Index