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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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.

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

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Simulation

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Sheldon M. Ross