## Description

The 5^{th} 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 5^{th} 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, 5^{th} edition presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.

### Key Features

New to this Edition:

- 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

## Details

- No. of pages:
- 328

- Language:
- English

- Copyright:
- © 2013

- Published:
- 22nd October 2012

- Imprint:
- Academic Press

- Print ISBN:
- 9780124158252

- Electronic ISBN:
- 9780124159716

## About the author

### Sheldon Ross

*Probability in the Engineering and Informational Sciences*. He is a Fellow of the Institute of Mathematical Statistics, and a recipient of the Humboldt US Senior Scientist Award.

#### Affiliations and Expertise

## 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.