Simulation / Sheldon M. Ross.
By: Ross, Sheldon M.
Contributor(s): Ross, Sheldon M. Course in simulation.
Material type: BookSeries: 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: 519.2Item 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 |
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)