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Simulation / Sheldon M. Ross.

By: Ross, Sheldon M.
Contributor(s): Ross, Sheldon M. Course in simulation.
Material type: materialTypeLabelBookSeries: Statistical modeling and decision science.Publisher: San Diego : Academic Press, c1997Edition: 2nd ed.Description: xii, 282 p. : ill ; 24 cm. + hbk.ISBN: 0125984103 .Subject(s): Random variables | Probabilities | Computer simulationDDC classification: 519.2
Contents:
Introduction -- Elements of probability -- Random numbers -- Generating discrete random variables -- Generating continuous random variables -- The discrete event simulation approach -- Statistical analysis of simulated data -- Variance reduction techniques -- Statistical validation techniques -- Markov chain Monte Carlo methods -- Some additional topics.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 519.2 (Browse shelf(Opens below)) 1 Available 00069049
Total holds: 0

Enhanced descriptions from Syndetics:

Simulation allows complex real world situations to be analyzed quantitatively. First, a model is created to represent the situation, then, using probability and statistics theory, the computer can perform a simulation to predict the outcome of this situation. This text provides a description of the generation of random variables and their use in analyzing a model in simulation study. It details how a computer may be used to generate random numbers, which may then be used to generate the behaviour of a stochastic model over time. The statistics needed to analyze simulated data and to validate the simulation model are also presented.

Rev. ed. of: A course in simulation. c1990.

Includes bibliographical references and index.

Introduction -- Elements of probability -- Random numbers -- Generating discrete random variables -- Generating continuous random variables -- The discrete event simulation approach -- Statistical analysis of simulated data -- Variance reduction techniques -- Statistical validation techniques -- Markov chain Monte Carlo methods -- Some additional topics.

Table of contents provided by Syndetics

  • Preface (p. ix)
  • 1 Introduction (p. 1)
  • Exercises (p. 3)
  • 2 Elements of Probability (p. 5)
  • 2.1 Sample Space and Events (p. 5)
  • 2.2 Axioms of Probability (p. 6)
  • 2.3 Conditional Probability and Independence (p. 7)
  • 2.4 Random Variables (p. 8)
  • 2.5 Expectation (p. 10)
  • 2.6 Variance (p. 13)
  • 2.7 Chebyshev's Inequality and the Laws of Large Numbers (p. 15)
  • 2.8 Some Discrete Random Variables (p. 17)
  • Binomial Random Variables (p. 17)
  • Poisson Random Variables (p. 18)
  • Geometric Random Variables (p. 20)
  • The Negative Binomial Random Variable (p. 20)
  • Hypergeometric Random Variables (p. 21)
  • 2.9 Continuous Random Variables (p. 22)
  • Uniformly Distributed Random Variables (p. 22)
  • Normal Random Variables (p. 23)
  • Exponential Random Variables (p. 25)
  • The Poisson Process and Gamma Random Variables (p. 27)
  • The Nonhomogeneous Poisson Process (p. 29)
  • 2.10 Conditional Expectation and Conditional Variance (p. 30)
  • Exercises (p. 32)
  • References (p. 36)
  • 3 Random Numbers (p. 37)
  • Introduction (p. 37)
  • 3.1 Pseudorandom Number Generation (p. 37)
  • 3.2 Using Random Numbers to Evaluate Integrals (p. 38)
  • Exercises (p. 42)
  • References (p. 44)
  • 4 Generating Discrete Random Variables (p. 45)
  • 4.1 The Inverse Transform Method (p. 45)
  • 4.2 Generating a Poisson Random Variable (p. 50)
  • 4.3 Generating Binomial Random Variables (p. 52)
  • 4.4 The Acceptance-Rejection Technique (p. 53)
  • 4.5 The Composition Approach (p. 55)
  • 4.6 Generating Random Vectors (p. 56)
  • Exercises (p. 57)
  • 5 Generating Continuous Random Variables (p. 63)
  • Introduction (p. 63)
  • 5.1 The Inverse Transform Algorithm (p. 63)
  • 5.2 The Rejection Method (p. 67)
  • 5.3 The Polar Method for Generating Normal Random Variables (p. 73)
  • 5.4 Generating a Poisson Process (p. 76)
  • 5.5 Generating a Nonhomogeneous Poisson Process (p. 77)
  • Exercises (p. 81)
  • References (p. 85)
  • 6 The Discrete Event Simulation Approach (p. 87)
  • Introduction (p. 87)
  • 6.1 Simulation via Discrete Events (p. 87)
  • 6.2 A Single-Server Queueing System (p. 88)
  • 6.3 A Queueing System with Two Servers in Series (p. 91)
  • 6.4 A Queueing System with Two Parallel Servers (p. 93)
  • 6.5 An Inventory Model (p. 96)
  • 6.6 An Insurance Risk Model (p. 97)
  • 6.7 A Repair Problem (p. 99)
  • 6.8 Exercising a Stock Option (p. 102)
  • 6.9 Verification of the Simulation Model (p. 103)
  • Exercises (p. 105)
  • References (p. 108)
  • 7 Statistical Analysis of Simulated Data (p. 109)
  • Introduction (p. 109)
  • 7.1 The Sample Mean and Sample Variance (p. 109)
  • 7.2 Interval Estimates of a Population Mean (p. 115)
  • 7.3 The Bootstrapping Technique for Estimating Mean Square Errors (p. 118)
  • Exercises (p. 124)
  • References (p. 127)
  • 8 Variance Reduction Techniques (p. 129)
  • Introduction (p. 129)
  • 8.1 The Use of Antithetic Variables (p. 131)
  • 8.2 The Use of Control Variates (p. 139)
  • 8.3 Variance Reduction by Conditioning (p. 147)
  • Estimating the Expected Number of Renewals by Time t (p. 155)
  • 8.4 Stratified Sampling (p. 157)
  • 8.5 Importance Sampling (p. 166)
  • 8.6 Using Common Random Numbers (p. 180)
  • 8.7 Evaluating an Exotic Option (p. 181)
  • Appendix Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions (p. 185)
  • Exercises (p. 188)
  • References (p. 195)
  • 9 Statistical Validation Techniques (p. 197)
  • Introduction (p. 197)
  • 9.1 Goodness of Fit Tests (p. 197)
  • The Chi-Square Goodness of Fit Test for Discrete Data (p. 198)
  • The Kolmogorov-Smirnov Test for Continuous Data (p. 200)
  • 9.2 Goodness of Fit Tests When Some Parameters Are Unspecified (p. 205)
  • The Discrete Data Case (p. 205)
  • The Continuous Data Case (p. 208)
  • 9.3 The Two-Sample Problem (p. 208)
  • 9.4 Validating the Assumption of a Nonhomogeneous Poisson Process (p. 215)
  • Exercises (p. 219)
  • References (p. 221)
  • 10 Markov Chain Monte Carlo Methods (p. 223)
  • Introduction (p. 223)
  • 10.1 Markov Chains (p. 223)
  • 10.2 The Hastings-Metropolis Algorithm (p. 226)
  • 10.3 The Gibbs Sampler (p. 228)
  • 10.4 Simulated Annealing (p. 239)
  • 10.5 The Sampling Importance Resampling Algorithm (p. 242)
  • Exercises (p. 246)
  • References (p. 249)
  • 11 Some Additional Topics (p. 251)
  • Introduction (p. 251)
  • 11.1 The Alias Method for Generating Discrete Random Variables (p. 251)
  • 11.2 Simulating a Two-Dimensional Poisson Process (p. 255)
  • 11.3 Simulation Applications of an Identity for Sums of Bernoulli Random Variables (p. 258)
  • 11.4 Estimating the Distribution and the Mean of the First Passage Time of a Markov Chain (p. 262)
  • 11.5 Coupling from the Past (p. 267)
  • Exercises (p. 269)
  • References (p. 271)
  • Index (p. 272)

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