Simulation
- 3rd Edition - December 27, 2001
- Latest edition
- Author: Sheldon M. Ross
- Language: English
Sheldon Ross' Simulation, Third Edition introduces aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing comput… Read more
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Sheldon Ross' Simulation, Third Edition introduces 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 new edition provides a comprehensive, in-depth, and current guide for constructing probability models and simulations for a variety of purposes. It features new information, including the presentation of the Insurance Risk Model, generating a Random Vector, and evaluating an Exotic Option. Also new is coverage of the changing nature of statistical methods due to the advancements in computing technology.
This new edition provides a comprehensive, in-depth, and current guide for constructing probability models and simulations for a variety of purposes. It features new information, including the presentation of the Insurance Risk Model, generating a Random Vector, and evaluating an Exotic Option. Also new is coverage of the changing nature of statistical methods due to the advancements in computing technology.
Researchers and practitioners in Computer Science, Industrial Engineering, Operations Research, Statistics, Mathematics, Electrical Engineering, Quantitative Business Analysis.
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
Binomial Random Variables
Poisson Random Variables
Geometric Random Variables
The Negative Binomial Random Variable
Hypergeometric Random Variables
2.9 Continuous Random Variables
Uniformly Distributed Random Variables
Normal Random Variables
Exponential Random Variables
The Poisson Process and Gamma Random Variables
The Nonhomogeneous Poisson Process
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 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
Exercises
References
6. The Discrete Event Simulation Approach
Introduction
6.1 Simulation via Discrete Events
6.2 A Single-Server Queueing System
6.3 A Queueing System with Two Servers in Series
6.4 A Queueing System with Two Parallel Servers
6.5 An Inventory Model
6.6 An Insurance Risk Model
6.7 A Repair Problem
6.8 Exercising a Stock Option
6.9 Verification of the Simulation Model
Exercises
References
7. Statistical Analysis of Simulated Data
Introduction
7.1 The Sample Mean and Sample Variance
7.2 Interval Estimates of a Population Mean
7.3 The Bootstrapping Technique for Estimating MeanSquare Errors
Exercises
References
8. Variance Reduction Techniques
Introduction
8.1 The Use of Antithetic Variables
8.2 The Use of Control Variates
8.3 Variance Reduction by Conditioning
Estimating the Expected Number of Renewals by Time A
8.4 Stratified Sampling
8.5 Importance Sampling
8.6 Using Common Random Numbers
8.7 Evaluating an Exotic Option
Appendix: Verification of Antithetic Variable ApproachWhen Estimating the Expected Value of Monotone
Functions
Exercises
References
9. Statistical Validation Techniques
Introduction
9.1 Goodness of Fit Tests
The Chi-Square Goodness of Fit Test for Discrete Data
The Kolmogorov-Smirnov Test for Continuous Data
9.2 Goodness of Fit Tests When Some Parameters Are Unspecified
The Discrete Data Case
The Continuous Data Case
9.3 The Two-Sample Problem
9.4 Validating the Assumption of a NonhomogeneousPoisson Process
Exercises
References
10. Markov Chain Monte Carlo Methods
Introduction
10.1 Markov Chains
10.2 The Hastings-Metropolis Algorithm
10.3 The Gibbs Sampler
10.4 Simulated Annealing
10.5 The Sampling Importance Resampling Algorithm
Exercises
References
11. Some Additional Topics
Introduction
11.1 The Alias Method for Generating DiscreteRandom Variables
11.2 Simulating a Two-Dimensional Poisson Process
11.3 Simulation Applications of an Identity for Sums of BernoulliRandom Variables
11.4 Estimating the Distribution and the Mean of the First PassageTime of a Markov Chain
11.5 Coupling from the Past
Exercises
References
Index
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
Binomial Random Variables
Poisson Random Variables
Geometric Random Variables
The Negative Binomial Random Variable
Hypergeometric Random Variables
2.9 Continuous Random Variables
Uniformly Distributed Random Variables
Normal Random Variables
Exponential Random Variables
The Poisson Process and Gamma Random Variables
The Nonhomogeneous Poisson Process
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 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
Exercises
References
6. The Discrete Event Simulation Approach
Introduction
6.1 Simulation via Discrete Events
6.2 A Single-Server Queueing System
6.3 A Queueing System with Two Servers in Series
6.4 A Queueing System with Two Parallel Servers
6.5 An Inventory Model
6.6 An Insurance Risk Model
6.7 A Repair Problem
6.8 Exercising a Stock Option
6.9 Verification of the Simulation Model
Exercises
References
7. Statistical Analysis of Simulated Data
Introduction
7.1 The Sample Mean and Sample Variance
7.2 Interval Estimates of a Population Mean
7.3 The Bootstrapping Technique for Estimating MeanSquare Errors
Exercises
References
8. Variance Reduction Techniques
Introduction
8.1 The Use of Antithetic Variables
8.2 The Use of Control Variates
8.3 Variance Reduction by Conditioning
Estimating the Expected Number of Renewals by Time A
8.4 Stratified Sampling
8.5 Importance Sampling
8.6 Using Common Random Numbers
8.7 Evaluating an Exotic Option
Appendix: Verification of Antithetic Variable ApproachWhen Estimating the Expected Value of Monotone
Functions
Exercises
References
9. Statistical Validation Techniques
Introduction
9.1 Goodness of Fit Tests
The Chi-Square Goodness of Fit Test for Discrete Data
The Kolmogorov-Smirnov Test for Continuous Data
9.2 Goodness of Fit Tests When Some Parameters Are Unspecified
The Discrete Data Case
The Continuous Data Case
9.3 The Two-Sample Problem
9.4 Validating the Assumption of a NonhomogeneousPoisson Process
Exercises
References
10. Markov Chain Monte Carlo Methods
Introduction
10.1 Markov Chains
10.2 The Hastings-Metropolis Algorithm
10.3 The Gibbs Sampler
10.4 Simulated Annealing
10.5 The Sampling Importance Resampling Algorithm
Exercises
References
11. Some Additional Topics
Introduction
11.1 The Alias Method for Generating DiscreteRandom Variables
11.2 Simulating a Two-Dimensional Poisson Process
11.3 Simulation Applications of an Identity for Sums of BernoulliRandom Variables
11.4 Estimating the Distribution and the Mean of the First PassageTime of a Markov Chain
11.5 Coupling from the Past
Exercises
References
Index
- Edition: 3
- Latest edition
- Published: January 12, 2002
- Language: English
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, USA