Simulation:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Amsterdam
Academic Press
2023
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Ausgabe: | Sixth edition |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis Klappentext |
Beschreibung: | xii, 320 Seiten Diagramme |
ISBN: | 9780323857390 |
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Datensatz im Suchindex
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adam_text | Contents Preface ,x 1 Introduction Exercises 1 3 2 Elements of probability 2.1 Sample space and events 2.2 Axioms of probability 2.3 Conditional probability and independence 2.4 Random variables 2.5 Expectation 2.6 Variance 2.7 Chebyshev’s inequality and the laws of large numbers 2.8 Some discrete random variables 2.9 Continuous random variables 2.10 Conditional expectation and conditional variance Exercises References 5 5 5 6 9 11 13 15 17 23 30 32 37 3 Random numbers Introduction 3.1 Pseudorandom number generation 3.2 Using random numbersto evaluate integrals Exercises References 39 39 39 40 44 45 4 Generating discrete random variables 4.1 The inverse transform method 4.2 Generating a Poisson random variable 4.3 Generating binomial random variables 4.4 The acceptance-rejection technique 4.5 The composition approach 4.6 The alias method for generating discrete random variables 4.7 Generating random vectors Exercises 47 47 53 54 55 57 59 62 63
Contents 5 Generating continuous random variables Introduction 5.1 The inverse transform algorithm 5.2 The rejection method 5.3 The polar method for generating normal random variables 5.4 Generating a Poisson process 5.5 Generating a nonhomogeneous Poisson process 5.6 Simulating a two-dimensional Poisson process Exercises References 69 69 69 73 82 86 87 90 94 97 6 The multivariate normal distribution and copulas Introduction 6.1 The multivariate normal 6.2 Generating a multivariate normal random vector 6.3 Copulas 6.4 Generating variables from copula models Exercises 99 99 99 101 104 109 109 7 The discrete event simulation approach Introduction 7.1 Simulation via discrete events 7.2 A single-server queueing system 7.3 A queueing system with two servers in series 7.4 A queueing system with two parallel servers 7.5 An inventory model 7.6 An insurance risk model 7.7 A repair problem 7.8 Exercising a stock option 7.9 Verification of the simulation model Exercises References 111 111 111 112 115 116 119 120 122 124 126 127 130 8 Statistical analysis of simulated data Introduction 8.1 The sample mean and sample variance 8.2 Interval estimates of a population mean 8.3 The bootstrapping technique for estimating mean square errors Exercises References 133 133 133 138 141 147 149 9 Variance reduction techniques Introduction 9.1 The use of antithetic variables 151 151 153
Contents The use of control variates Variance reduction by conditioning Stratified sampling Applications of stratified sampling Importance sampling Using common random numbers Evaluating an exotic option Appendix: Verification of antithetic variable approach when estimating the expected value of monotone functions Exercises References 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 Additional variance reduction techniques Introduction 10.1 The conditional Bernoulli sampling method 10.2 A simulation estimator based on an identity of Chen-Stein 10.3 Using random hazards 10.4 Normalized importance sampling 10.5 Latin hypercube sampling Exercises 11 Statistical validation techniques Introduction 11.1 Goodness of fit tests 11.2 Goodness of fit tests when some parameters are unspecified 11.3 The two-sample problem 11.4 Validating the assumption of a nonhomogeneous Poisson process Exercises References 12 Markov chain Monte Carlo methods Introduction 12.1 Markov chains 12.2 The Hastings-Metropolis algorithm 12.3 The Gibbs sampler 12.4 Continuous time Markov chains and a queueing loss model 12.5 Simulated annealing 12.6 The sampling importance resampling algorithm 12.7 Coupling from the past Exercises References Index vu 160 166 180 190 199 212 213 217 219 227 229 229 229 233 241 246 250 252 255 255 255 262 265 271 275 277 279 279 279 282 284 294 298 300 304 306 308 311
SIMULATION Now in its sixth edition. Sheldon Ross s · continues aspiring and practicing actuaries, engineers, computer s; others to the practical aspects of constructing computerize studies to analyze and interpret real phenomena. Reac apply results of these analyses to problems in a wide varie obtain effective, accurate solutions and make predictions tcomes By explaining now a computer can be used to generate random numbers and how to use these random numbers to generate the behavior of a stochastic model over time. Ross s presents the statistics needed to analyze simulated data as wet as that needed for vahdatina the simulation moder
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adam_txt |
Contents Preface ,x 1 Introduction Exercises 1 3 2 Elements of probability 2.1 Sample space and events 2.2 Axioms of probability 2.3 Conditional probability and independence 2.4 Random variables 2.5 Expectation 2.6 Variance 2.7 Chebyshev’s inequality and the laws of large numbers 2.8 Some discrete random variables 2.9 Continuous random variables 2.10 Conditional expectation and conditional variance Exercises References 5 5 5 6 9 11 13 15 17 23 30 32 37 3 Random numbers Introduction 3.1 Pseudorandom number generation 3.2 Using random numbersto evaluate integrals Exercises References 39 39 39 40 44 45 4 Generating discrete random variables 4.1 The inverse transform method 4.2 Generating a Poisson random variable 4.3 Generating binomial random variables 4.4 The acceptance-rejection technique 4.5 The composition approach 4.6 The alias method for generating discrete random variables 4.7 Generating random vectors Exercises 47 47 53 54 55 57 59 62 63
Contents 5 Generating continuous random variables Introduction 5.1 The inverse transform algorithm 5.2 The rejection method 5.3 The polar method for generating normal random variables 5.4 Generating a Poisson process 5.5 Generating a nonhomogeneous Poisson process 5.6 Simulating a two-dimensional Poisson process Exercises References 69 69 69 73 82 86 87 90 94 97 6 The multivariate normal distribution and copulas Introduction 6.1 The multivariate normal 6.2 Generating a multivariate normal random vector 6.3 Copulas 6.4 Generating variables from copula models Exercises 99 99 99 101 104 109 109 7 The discrete event simulation approach Introduction 7.1 Simulation via discrete events 7.2 A single-server queueing system 7.3 A queueing system with two servers in series 7.4 A queueing system with two parallel servers 7.5 An inventory model 7.6 An insurance risk model 7.7 A repair problem 7.8 Exercising a stock option 7.9 Verification of the simulation model Exercises References 111 111 111 112 115 116 119 120 122 124 126 127 130 8 Statistical analysis of simulated data Introduction 8.1 The sample mean and sample variance 8.2 Interval estimates of a population mean 8.3 The bootstrapping technique for estimating mean square errors Exercises References 133 133 133 138 141 147 149 9 Variance reduction techniques Introduction 9.1 The use of antithetic variables 151 151 153
Contents The use of control variates Variance reduction by conditioning Stratified sampling Applications of stratified sampling Importance sampling Using common random numbers Evaluating an exotic option Appendix: Verification of antithetic variable approach when estimating the expected value of monotone functions Exercises References 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 Additional variance reduction techniques Introduction 10.1 The conditional Bernoulli sampling method 10.2 A simulation estimator based on an identity of Chen-Stein 10.3 Using random hazards 10.4 Normalized importance sampling 10.5 Latin hypercube sampling Exercises 11 Statistical validation techniques Introduction 11.1 Goodness of fit tests 11.2 Goodness of fit tests when some parameters are unspecified 11.3 The two-sample problem 11.4 Validating the assumption of a nonhomogeneous Poisson process Exercises References 12 Markov chain Monte Carlo methods Introduction 12.1 Markov chains 12.2 The Hastings-Metropolis algorithm 12.3 The Gibbs sampler 12.4 Continuous time Markov chains and a queueing loss model 12.5 Simulated annealing 12.6 The sampling importance resampling algorithm 12.7 Coupling from the past Exercises References Index vu 160 166 180 190 199 212 213 217 219 227 229 229 229 233 241 246 250 252 255 255 255 262 265 271 275 277 279 279 279 282 284 294 298 300 304 306 308 311
SIMULATION Now in its sixth edition. Sheldon Ross s · continues aspiring and practicing actuaries, engineers, computer s; others to the practical aspects of constructing computerize studies to analyze and interpret real phenomena. Reac apply results of these analyses to problems in a wide varie obtain effective, accurate solutions and make predictions tcomes By explaining now a computer can be used to generate random numbers and how to use these random numbers to generate the behavior of a stochastic model over time. Ross s presents the statistics needed to analyze simulated data as wet as that needed for vahdatina the simulation moder |
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spelling | Ross, Sheldon M. 1943- Verfasser (DE-588)123762235 aut Simulation Sheldon M. Ross (Epstein Department of Industrial and Systems Engineering, University of South California, Los Angeles, CA, United States) Sixth edition Amsterdam Academic Press 2023 © 2023 xii, 320 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier aRandom variables aProbabilities aComputer simulation Computersimulation (DE-588)4148259-1 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Computersimulation (DE-588)4148259-1 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Simulation (DE-588)4055072-2 s Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034009894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034009894&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
spellingShingle | Ross, Sheldon M. 1943- Simulation aRandom variables aProbabilities aComputer simulation Computersimulation (DE-588)4148259-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Simulation (DE-588)4055072-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
subject_GND | (DE-588)4148259-1 (DE-588)4240945-7 (DE-588)4055072-2 (DE-588)4064324-4 |
title | Simulation |
title_auth | Simulation |
title_exact_search | Simulation |
title_exact_search_txtP | Simulation |
title_full | Simulation Sheldon M. Ross (Epstein Department of Industrial and Systems Engineering, University of South California, Los Angeles, CA, United States) |
title_fullStr | Simulation Sheldon M. Ross (Epstein Department of Industrial and Systems Engineering, University of South California, Los Angeles, CA, United States) |
title_full_unstemmed | Simulation Sheldon M. Ross (Epstein Department of Industrial and Systems Engineering, University of South California, Los Angeles, CA, United States) |
title_short | Simulation |
title_sort | simulation |
topic | aRandom variables aProbabilities aComputer simulation Computersimulation (DE-588)4148259-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Simulation (DE-588)4055072-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
topic_facet | aRandom variables aProbabilities aComputer simulation Computersimulation Monte-Carlo-Simulation Simulation Wahrscheinlichkeitsrechnung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034009894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034009894&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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