Essentials of Monte Carlo simulation statistical methods for building simulation models Nick T. Thomopoulos

Format:

Book

Author/Creator:

Thomopoulos, Nicholas T.

Language:

English

Subjects (All):

Monte Carlo method.

Statistics.

Statistical Theory and Methods.

Statistics and Computing/Statistics Programs.

Statistics, general.

statistics.

Local Subjects:

Statistics.

Statistical Theory and Methods.

Statistics and Computing/Statistics Programs.

Statistics, general.

Physical Description:

1 online resource

Place of Publication:

New York Springer ©2013

Language Note:

English

System Details:

PDF

text file

Summary:

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 using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run very many times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. More than 100 numerical examples are presented in the chapters to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. With a strong focus in the area of computer Monte Carlo simulation methods, this book will appeal to students and researchers in the fields of Mathematics and Statistics. Nick T. Thomopoulos is a professor emeritus at the Illinois Institute of Technology. He is the author of six books, including Fundamentals of Queuing Systems (2012). He has more than 100 published papers and presentations to his credit, and for many years, he has consulted in a wide variety of industries in the United States, Europe, and Asia. He has been the recipient of numerous honors, such as the Rist Prize in 1972 from the Military Operations Research Society for new developments in queuing theory, the Distinguished Professor Award in Bangkok, Thailand in 2005 from the IIT Asian Alumni Association, and the Professional Achievement Award in 2009 from the IIT Alumni Association

Contents:

Random Number Generators Generating Random Variates Generating Continuous Random Variates Generating Discrete Random Variates Generating Multivariate Random Variates Special Applications Output from Simulation Runs Analysis of Output Data Choosing the Probability Distribution from Data Choosing the Probability Distribution When No Data

Machine generated contents note: 1. Introduction Monte Carlo Method Random Number Generators Computer Languages Computer Simulation Software Basic Fundamentals Chapter Summaries

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

3. Generating Random Variates Introduction 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

4. Generating Continuous Random Variates Introduction Continuous Uniform Exponential Standard Exponential Erlang Gamma When k <1 When k> 1 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

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

6. Generating Multivariate Random Variates Introduction 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

7. Special Applications Introduction 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

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 Cyclical Partitions and Buffers Other Models Forecasting Database Forecast and Replenish Database Summary

9. Analysis of Output Data Introduction Variable Type Data Proportion Type Data Analysis of Variable Type Data Sample Mean and Variance Confidence Interval of μ when x is Normal Approximate Confidence Interval of μ when x is Not Normal Central Limit Theorem When Need More Accuracy Analysis of Proportion Type Data Proportion Estimate and Its Variance Confidence Interval of p When Need More Accuracy Comparing Two Options Comparing Two Means when Variable Type Data Comparing x1 and x2 Confidence Interval of (μ1

μ2) when Normal Distribution Significant Test When σ1 = σ2 When σ1 [≠] σ2 Approximate Confidence Interval of (μ1

μ2) when Not Normal As Degrees of Freedom Increases Comparing the Proportions Between Two Options Comparing p1 and p2 Confidence Interval of (p1

p2) Significant Test Comparing k Means of Variable Type Data One-Way Analysis of Variance Summary

10. Choosing the Probability Distribution from Data Introduction Collecting the Data Test for Independence Autocorrelation Some Useful Statistical Measures Location Parameter Candidate Probability Distributions Transforming Variables Transform Data to (0,1) Transform Data to (x [≥] 0) Candidate Continuous Distributions Continuous Uniform Normal Exponential Lognormal Gamma Beta Weibull Some Candidate Discrete Distributions Discrete Uniform Binomial Geometric Pascal Poisson Estimating Parameters for Continuous Distributions Continuous Uniform Normal Distribution Exponential Lognormal Gamma Beta Estimating Parameters for Discrete Distributions Discrete Uniform Binomial Geometric Pascal Poisson

Q-Q Plot

P-P Plot Adjustment for Ties Summary

11. Choosing the Probability Distribution When No Data Introduction Continuous Uniform Triangular Beta Lognormal Weibull Solving for k1 Solving for k2 Summary

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Thomopoulos, Nick T. Essentials of monte carlo simulation

ISBN:

9781461460220

1461460220

1461460212

9781461460213

128394605X

9781283946056

OCLC:

823514232

Access Restriction:

Restricted for use by site license