Simulation

ISBN-10: 0124158250
ISBN-13: 9780124158252
Edition: 5th 2012
Authors: Sheldon Ross
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Description: Ross's Simulation, Fifth 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  More...

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Book details

List price: $60.99
Edition: 5th
Copyright year: 2012
Publisher: Elsevier Science & Technology
Publication date: 12/7/2012
Binding: Hardcover
Pages: 328
Size: 6.25" wide x 9.25" long x 0.10" tall
Weight: 1.122
Language: English

Ross's Simulation, Fifth 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 text explains 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. It presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model. 

Preface
Introduction
Exercises
Elements of Probability
Sample Space and Events
Axioms of Probability
Conditional Probability and Independence
Random Variables
Expectation
Variance
Chebyshev's Inequality and the Laws of Large Numbers
Some Discrete Random Variables
Continuous Random Variables
Conditional Expectation and Conditional Variance
Exercises
Bibliography
Random Numbers
Introduction
Pseudorandom Number Generation
Using Random Numbers to Evaluate Integrals
Exercises
Bibliography
Generating Discrete Random Variables
The Inverse Transform Method
Generating a Poisson Random Variable
Generating Binomial Random Variables
The Acceptance-Rejection Technique
The Composition Approach
The Alias Method for Generating Discrete Random Variables
Generating Random Vectors
Exercises
Generating Continuous Random Variables
Introduction
The Inverse Transform Algorithm
The Rejection Method
The Polar Method for Generating Normal Random Variables
Generating a Poisson Process
Generating a Nonhomogeneous Poisson Process
Simulating a Two-Dimensional Poisson Process
Exercises
Bibliography
The Multivariate Normal Distribution and Copulas
Introduction
The Multivariate Normal
Generating a Multivariate Normal Random Vector
Copulas
Generating Variables from Copula Models
Exercises
The Discrete Event Simulation Approach
Introduction
Simulation via Discrete Events
A Single-Server Queueing System
A Queueing System with Two Servers in Series
A Queueing System with Two Parallel Servers
An Inventory Model
An Insurance Risk Model
A Repair Problem
Exercising a Stock Option
Verification of the Simulation Model
Exercises
Bibliography
Statistical Analysis of Simulated Data
Introduction
The Sample Mean and Sample Variance
Interval Estimates of a Population Mean
The Bootstrapping Technique for Estimating Mean Square Errors
Exercises
Bibliography
Variance Reduction Techniques
Introduction
The Use of Antithetic Variables
The Use of Control Variates
Variance Reduction by Conditioning
Stratified Sampling
Applications of Stratified Sampling
Importance Sampling
Using Common Random Numbers
Evaluating an Exotic Option
Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions
Exercises
Bibliography
Additional Variance Reduction Techniques
Introduction
The Conditional Bernoulli Sampling Method
Normalized Importance Sampling
Latin Hypercube Sampling
Exercises
Statistical Validation Techniques
Introduction
Goodness of Fit Tests
Goodness of Fit Tests When Some Parameters Are Unspecified
The Two-Sample Problem
Validating the Assumption of a Nonhomogeneous Poisson Process
Exercises
Bibliography
Markov Chain Monte Carlo Methods
Introduction
Markov Chains
The Hastings-Metropolis Algorithm
The Gibbs Sampler
Continuous time Markov Chains and a Queueing Loss Model
Simulated Annealing
The Sampling Importance Resampling Algorithm
Coupling from the Past
Exercises
Bibliography
Index

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