Essentials of Monte Carlo Simulation : Statistical Methods for Building Simulation Models.

Essentials of Monte Carlo Simulation : Statistical Methods for Building Simulation Models.

Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs usi...

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Bibliographic Details
Main Author: Thomopoulos, Nick T.
Format: eBook
Language:English
Published: Dordrecht : Springer, 2012.
Subjects:
Mathematical statistics.
Statistics.
statistics.
Mathematical statistics
Statistics
Online Access:Click for online access
Table of Contents:
  • Essentials of Monte Carlo Simulation; Preface; Time Series Forecasting; Order Quantity; Safety Stock; Production; Other; Acknowledgments; Contents; Chapter 1: Introduction; Monte Carlo Method; Random Number Generators; Computer Languages; Computer Simulation Software; Basic Fundamentals; Chapter Summaries; Chapter 2: Random Number Generators; Introduction; Modular Arithmetic; Linear Congruent Generators; Generating Uniform Variates; 32-Bit Word Length; Random Number Generator Tests; Length of the Cycle; Mean and Variance; Chi Square; Autocorrelation; Pseudo Random Numbers; Summary.
  • Chapter 3: Generating Random VariatesIntroduction; Inverse Transform Method; Continuous Variables; Discrete Variables; Accept-Reject Method; Truncated Variables; Order Statistics; Sorted Values; Minimum Value; Maximum Value; Composition; Summation; Triangular Distribution; Empirical Ungrouped Data; Empirical Grouped Data; Summary; Chapter 4: Generating Continuous Random Variates; Introduction; Continuous Uniform; Exponential; Standard Exponential; Erlang; Gamma; When k1; When k1; Beta; Standard Beta; Weibull; Normal Distribution; Hastings Approximation of F(z) from z.
  • Hastings Approximation of z from F(z)Hastings Method; Convolution Method; Sine-Cosine Method; Lognormal; Chi-Square; Approximation Formula; Relation to Gamma; Generate a Random Chi-Square Variate; Student ́s t; Generate a Random Variate; Fishers ́ F; Summary; Chapter 5: Generating Discrete Random Variates; Introduction; Discrete Arbitrary; Discrete Uniform; Bernoulli; Binomial; When n is Small; Normal Approximation; Poisson Approximation; Hyper Geometric; Geometric; Pascal; Poisson; Relation to the Exponential Distribution; Generating a Random Poisson Variate; Summary.
  • Chapter 6: Generating Multivariate Random VariatesIntroduction; Multivariate Discrete Arbitrary; Generate a Random Set of Variates; Multinomial; Generating Random Multinomial Variates; Multivariate Hyper Geometric; Generating Random Variates; Bivariate Normal; Marginal Distributions; Conditional Distributions; Generate Random Variates (x1, x2); Bivariate Lognormal; Generate a Random Pair (x1, x2); Multivariate Normal; Cholesky Decomposition; Generate a Random Set [x1, , xk]; Multivariate Lognormal; Cholesky Decomposition; Generate a Random Set [x1, , xk]; Summary.
  • Chapter 7: Special ApplicationsIntroduction; Poisson Process; Constant Poisson Process; Batch Arrivals; Active Redundancy; Generate a Random Variate; Standby Redundancy; Generate a Random Variate; Random Integers Without Replacement; Generate a Random Sequence; Poker; Generate Random Hands to Players A and B; Summary; Chapter 8: Output from Simulation Runs; Introduction; Terminating System; Nonterminating Transient Equilibrium Systems; Identifying the End of the Transient Stage; Output Data; Partitions and Buffers; Nonterminating Transient Cyclical Systems; Output Data.

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