# Simulation

## 5th Edition

**Authors:**Sheldon Ross

**eBook ISBN:**9780124159716

**Hardcover ISBN:**9780124158252

**Imprint:**Academic Press

**Published Date:**22nd October 2012

**Page Count:**328

## 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

## Details

- No. of pages:
- 328

- Language:
- English

- Copyright:
- © Academic Press 2013

- Published:
- 22nd October 2012

- Imprint:
- Academic Press

- eBook ISBN:
- 9780124159716

- Hardcover ISBN:
- 9780124158252

## About the Author

### 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 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, a Fellow of INFORMS, and a recipient of the Humboldt US Senior Scientist Award.

### Affiliations and Expertise

University of Southern California, Los Angeles, USA

## 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**