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PRINTED BOOKS
Author Ross, Sheldon M.

Title Simulation / Sheldon M. Ross.

Published San Diego : Academic Press, [2002]
©2002

Copies

Location Call No. Status
 UniM Bund  003.760113 ROSS {Bund89 20200519}    AVAILABLE
Edition 3rd ed.
Physical description xiii, 274 pages : illustrations ; 24 cm
Bibliography Includes bibliographical references and index.
Contents 2 Elements of Probability 5 -- 2.1 Sample Space and Events 5 -- 2.2 Axioms of Probability 6 -- 2.3 Conditional Probability and Independence 7 -- 2.4 Random Variables 8 -- 2.5 Expectation 10 -- 2.6 Variance 13 -- 2.7 Chebyshev's Inequality and the Laws of Large Numbers 15 -- 2.8 Some Discrete Random Variables 17 -- 2.9 Continuous Random Variables 22 -- 2.10 Conditional Expectation and Conditional Variance 30 -- 3 Random Numbers 37 -- 3.1 Pseudorandom Number Generation 37 -- 3.2 Using Random Numbers to Evaluate Integrals 38 -- 4 Generating Discrete Random Variables 45 -- 4.1 Inverse Transform Method 45 -- 4.2 Generating a Poisson Random Variable 50 -- 4.3 Generating Binomial Random Variables 52 -- 4.4 Acceptance-Rejection Technique 53 -- 4.5 Composition Approach 55 -- 4.6 Generating Random Vectors 56 -- 5 Generating Continuous Random Variables 63 -- 5.1 Inverse Transform Algorithm 63 -- 5.2 Rejection Method 67 -- 5.3 Polar Method for Generating Normal Random Variables 73 -- 5.4 Generating a Poisson Process 76 -- 5.5 Generating a Nonhomogeneous Poisson Process 77 -- 6 Discrete Event Simulation Approach 87 -- 6.1 Simulation via Discrete Events 87 -- 6.2 A Single-Server Queueing System 88 -- 6.3 A Queueing System with Two Servers in Series 91 -- 6.4 A Queueing System with Two Parallel Servers 93 -- 6.5 An Inventory Model 96 -- 6.6 An Insurance Risk Model 97 -- 6.7 A Repair Problem 99 -- 6.8 Exercising a Stock Option 102 -- 6.9 Verification of the Simulation Model 103 -- 7 Statistical Analysis of Simulated Data 109 -- 7.1 Sample Mean and Sample Variance 109 -- 7.2 Interval Estimates of a Population Mean 115 -- 7.3 Bootstrapping Technique for Estimating Mean Square Errors 118 -- 8 Variance Reduction Techniques 129 -- 8.1 Use of Antithetic Variables 131 -- 8.2 Use of Control Variates 139 -- 8.3 Variance Reduction by Conditioning 147 -- 8.4 Stratified Sampling 157 -- 8.5 Importance Sampling 166 -- 8.6 Using Common Random Numbers 180 -- 8.7 Evaluating an Exotic Option 181 -- Appendix Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions 185 -- 9 Statistical Validation Techniques 197 -- 9.1 Goodness of Fit Tests 197 -- 9.2 Goodness of Fit Tests When Some Parameters Are Unspecified 205 -- 9.3 Two-Sample Problem 208 -- 9.4 Validating the Assumption of a Nonhomogeneous Poisson Process 215 -- 10 Markov Chain Monte Carlo Methods 223 -- 10.1 Markov Chains 223 -- 10.2 Hastings-Metropolis Algorithm 226 -- 10.3 Gibbs Sampler 228 -- 10.4 Simulated Annealing 239 -- 10.5 Sampling Importance Resampling Algorithm 242 -- 11.1 Alias Method for Generating Discrete Random Variables 251 -- 11.2 Simulating a Two-Dimensional Poisson Process 255 -- 11.3 Simulation Applications of an Identity for Sums of Bernoulli Random Variables 258 -- 11.4 Estimating the Distribution and the Mean of the First Passage Time of a Markov Chain 262 -- 11.5 Coupling from the Past 267.
Summary 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 adaptation of Sheldon Ross' best-selling Simulation provides a comprehensive, in-depth, and current guide for constructing probability models and simulations for a variety of purposes. This edition 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 in practice due to the advancements in computing technology.
Subject Random variables.
Probabilities.
Computer simulation.
ISBN 0125980531 (alk. paper)