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Simulation

Auteur: Sheldon M Ross
Uitgever: Amsterdam ; Boston : Elsevier Academic Press, ©2006.
Editie/Formaat:   Boek : Engels : 4th edAlle edities en materiaalsoorten bekijken.
Database:WorldCat
Samenvatting:

Introduces practising actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. This text  Meer lezen...

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Details

Genre: Internetbron
Soort document: Boek, Internetbron
Alle auteurs / medewerkers: Sheldon M Ross
ISBN: 0125980639 9780125980630
OCLC-nummer: 69672100
Beschrijving: xiii, 298 p. : ill. ; 24 cm.
Inhoud: 2 Elements of Probability 5 --
2.1 Sample Space and Events 5 --
2.2 Axioms of Probability 6 --
2.3 Conditional Probability and Independence 7 --
2.4 Random Variables 9 --
2.5 Expectation 11 --
2.6 Variance 14 --
2.7 Chebyshev's Inequality and the Laws of Large Numbers 16 --
2.8 Some Discrete Random Variables 18 --
Binomial Random Variables 18 --
Poisson Random Variables 20 --
Geometric Random Variables 22 --
The Negative Binomial Random Variable 23 --
Hypergeometric Random Variables 24 --
2.9 Continuous Random Variables 24 --
Uniformly Distributed Random Variables 25 --
Normal Random Variables 26 --
Exponential Random Variables 27 --
The Poisson Process and Gamma Random Variables 29 --
The Nonhomogeneous Poisson Process 32 --
2.10 Conditional Expectation and Conditional Variance 33 --
The Conditional Variance Formula 34 --
3 Random Numbers 41 --
3.1 Pseudorandom Number Generation 41 --
3.2 Using Random Numbers to Evaluate Integrals 42 --
4 Generating Discrete Random Variables 49 --
4.1 The Inverse Transform Method 49 --
4.2 Generating a Poisson Random Variable 55 --
4.3 Generating Binomial Random Variables 57 --
4.4 The Acceptance-Rejection Technique 58 --
4.5 The Composition Approach 60 --
4.6 Generating Random Vectors 61 --
5 Generating Continuous Random Variables 67 --
5.1 The Inverse Transform Algorithm 67 --
5.2 The Rejection Method 71 --
5.3 The Polar Method for Generating Normal Random Variables 78 --
5.4 Generating a Poisson Process 82 --
5.5 Generating a Nonhomogeneous Poisson Process 83 --
6 The Discrete Event Simulation Approach 93 --
6.1 Simulation via Discrete Events 93 --
6.2 A Single-Server Queueing System 94 --
6.3 A Queueing System with Two Servers in Series 97 --
6.4 A Queueing System with Two Parallel Servers 99 --
6.5 An Inventory Model 102 --
6.6 An Insurance Risk Model 103 --
6.7 A Repair Problem 105 --
6.8 Exercising a Stock Option 108 --
6.9 Verification of the Simulation Model 110 --
7 Statistical Analysis of Simulated Data 117 --
7.1 The Sample Mean and Sample Variance 117 --
7.2 Interval Estimates of a Population Mean 123 --
7.3 The Bootstrapping Technique for Estimating Mean Square Errors 126 --
8 Variance Reduction Techniques 137 --
8.1 The Use of Antithetic Variables 139 --
8.2 The Use of Control Variates 147 --
8.3 Variance Reduction by Conditioning 154 --
Estimating the Expected Number of Renewals by Time t 164 --
8.4 Stratified Sampling 166 --
8.5 Applications of Stratified Sampling 175 --
Analyzing Systems Having Poisson Arrivals 176 --
Computing Multidimensional Integrals of Monotone Functions 180 --
Compound Random Vectors 182 --
8.6 Importance Sampling 184 --
8.7 Using Common Random Numbers 197 --
8.8 Evaluating an Exotic Option 198 --
8.9 Estimating Functions of Random Permutations and Random Subsets 203 --
Random Permutations 203 --
Random Subsets 206 --
8.10 Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions 207 --
9 Statistical Validation Techniques 219 --
9.1 Goodness of Fit Tests 219 --
The Chi-Square Goodness of Fit Test for Discrete Data 220 --
The Kolmogorov-Smirnov Test for Continuous Data 222 --
9.2 Goodness of Fit Tests When Some Parameters Are Unspecified 227 --
The Discrete Data Case 227 --
The Continuous Data Case 230 --
9.3 The Two-Sample Problem 230 --
9.4 Validating the Assumption of a Nonhomogeneous Poisson Process 237 --
10 Markov Chain Monte Carlo Methods 245 --
10.1 Markov Chains 245 --
10.2 The Hastings-Metropolis Algorithm 248 --
10.3 The Gibbs Sampler 251 --
10.4 Simulated Annealing 262 --
10.5 The Sampling Importance Resampling Algorithm 264 --
11 Some Additional Topics 273 --
11.1 The Alias Method for Generating Discrete Random Variables 273 --
11.2 Simulating a Two-Dimensional Poisson Process 277 --
11.3 Simulation Applications of an Identity for Sums of Bernoulli Random Variables 280 --
11.4 Estimating the Distribution and the Mean of the First Passage Time of a Markov Chain 285 --
11.5 Coupling from the Past 289.
Verantwoordelijkheid: Sheldon M. Ross.
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"His is a book that makes a very serious effort to go in the same direction as the changes in computing technology. To the best of my knowledge this is the only teaching book on simulation. It is Meer lezen...

 
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