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# Simulation

- 6th Edition - June 14, 2022
- Author: Sheldon M. Ross
- Language: English
- Hardback ISBN:9 7 8 - 0 - 3 2 3 - 8 5 7 3 9 - 0
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 8 9 9 6 1 - 1

Simulation, Sixth Edition continues to introduce aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing comput… Read more

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Request a sales quote*Simulation, Sixth Edition*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 will learn to apply the results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions. 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, this book presents the statistics needed to analyze simulated data and validate simulation models.

- Includes updated content throughout
- Offers a wealth of practice exercises as well as applied use of free software package R
- Features the author’s well-known, award-winning and accessible approach to complex information

- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Overview
- New to this edition
- Chapter descriptions
- Thanks
- 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
- References
- 3: Random numbers
- Introduction
- 3.1. Pseudorandom number generation
- 3.2. Using random numbers to evaluate integrals
- Exercises
- References
- 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
- References
- 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
- 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
- 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
- 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
- 10: Additional variance reduction techniques
- Introduction
- 10.1. The conditional Bernoulli sampling method
- 10.2. A simulation estimator based on an identity of Chen–Stein
- 10.3. Using random hazards
- 10.4. Normalized importance sampling
- 10.5. Latin hypercube sampling
- Exercises
- 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
- 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 queueing loss model
- 12.5. Simulated annealing
- 12.6. The sampling importance resampling algorithm
- 12.7. Coupling from the past
- Exercises
- References
- Index

- No. of pages: 336
- Language: English
- Edition: 6
- Published: June 14, 2022
- Imprint: Academic Press
- Hardback ISBN: 9780323857390
- eBook ISBN: 9780323899611

SR

### Sheldon M. Ross

Dr. Sheldon M. Ross is a professor in the Department of Industrial and Systems Engineering at the University of Southern California. He received his PhD 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, a Fellow of INFORMS, and a recipient of the Humboldt US Senior Scientist Award.

Affiliations and expertise

Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USARead

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