Simulation

Simulation

5th Edition - October 22, 2012

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  • Author: Sheldon Ross
  • Hardcover ISBN: 9780124158252
  • eBook ISBN: 9780124159716

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Description

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.

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

Readership

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

Table of Contents

  • 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

Product details

  • No. of pages: 328
  • Language: English
  • Copyright: © Academic Press 2012
  • Published: October 22, 2012
  • Imprint: Academic Press
  • Hardcover ISBN: 9780124158252
  • eBook ISBN: 9780124159716

About the Author

Sheldon Ross

Sheldon 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

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