Simulation, 5th Edition

Simulation, 5th Edition,Sheldon Ross,ISBN9780124158252


Academic Press




229 X 152

This reference shows the reader 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 as well as presenting the statistics needed to analyze simulated data and the simulation model

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Key Features

  • 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


The 5th 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 5th 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, 5th edition presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.


Senior/graduate level students taking a course in Simulation, found in many different departments, including: Computer Science, Industrial Engineering, Operations Research, Statistics, Mathematics, Electrical Engineering, and Quantitative Business Analysis

Sheldon Ross

Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences. He is a Fellow of the Institute of Mathematical Statistics, and a recipient of the Humboldt US Senior Scientist Award.

Affiliations and Expertise

University of Southern California, Los Angeles, USA

View additional works by Sheldon M. Ross

Simulation, 5th Edition



New to This Edition

Chapter Descriptions


Chapter 1. Introduction


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



Chapter 3. Random Numbers


3.1 Pseudorandom Number Generation

3.2 Using Random Numbers to Evaluate Integrals



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


Chapter 5. Generating Continuous Random Variables


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



Chapter 6. The Multivariate Normal Distribution and Copulas


6.1 The Multivariate Normal

6.2 Generating a Multivariate Normal Random Vector

6.3 Copulas

6.4 Generating Variables from Copula Models


Chapter 7. The Discrete Event Simulation Approach


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



Chapter 8. Statistical Analysis of Simulated Data


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



Chapter 9. Variance Reduction Techniques


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



Chapter 10. Additional Variance Reduction Techniques


2 The Conditional Bernoulli Sampling Method

3 Normalized Importance Sampling

4 Latin Hypercube Sampling


Chapter 11. Statistical Validation Techniques


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



Chapter 12. Markov Chain Monte Carlo Methods


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




Quotes and 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


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