LEADER 06397nam 2200613 a 450 001 9910438154803321 005 20200520144314.0 010 $a1-283-94605-X 010 $a1-4614-6022-0 024 7 $a10.1007/978-1-4614-6022-0 035 $a(CKB)2670000000316194 035 $a(EBL)1082061 035 $a(OCoLC)823388530 035 $a(SSID)ssj0000810880 035 $a(PQKBManifestationID)11494982 035 $a(PQKBTitleCode)TC0000810880 035 $a(PQKBWorkID)10854323 035 $a(PQKB)11788947 035 $a(DE-He213)978-1-4614-6022-0 035 $a(MiAaPQ)EBC1082061 035 $a(PPN)168304511 035 $a(EXLCZ)992670000000316194 100 $a20130108d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEssentials of Monte Carlo simulation $estatistical methods for building simulation models /$fNick T. Thomopoulos 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (183 p.) 300 $aDescription based upon print version of record. 311 $a1-4899-8608-1 311 $a1-4614-6021-2 320 $aIncludes bibliographical references and index. 327 $aEssentials 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 327 $aChapter 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; 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 327 $aHastings 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 327 $aChapter 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 327 $aChapter 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; 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 327 $aCyclical Partitions and Buffers 330 $aEssentials 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. 606 $aMonte Carlo method 615 0$aMonte Carlo method. 676 $a519.5 700 $aThomopoulos$b Nick T$0767476 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438154803321 996 $aEssentials of Monte Carlo Simulation$92502990 997 $aUNINA