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E-raamat: Simulation

(Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USA)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 14-Jun-2022
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780323899611
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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 14-Jun-2022
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780323899611
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Simulation, Sixth Edition continues to introduce aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers will learn to apply the results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions. By explaining how 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, this book presents the statistics needed to analyze simulated data and validate simulation models.
  • Includes updated content throughout
  • Offers a wealth of practice exercises as well as applied use of free software package R
  • Features the author’s well-known, award-winning and accessible approach to complex information

Arvustused

"This textbook contains and describes all the tools one needs to plan and to carry out a simulation study as well as to analyze its results." --J.Wolters, zbMATH Open

"It presents the statistics needed to analyze simulated data and to validate the simulation model. In this edition, several new topics are included as well as a number of new exercises." --Vigirdas Mackeviius, zbMATH Open

Preface ix
1 Introduction
1(4)
Exercises
3(2)
2 Elements of probability
5(34)
2.1 Sample space and events
5(1)
2.2 Axioms of probability
5(1)
2.3 Conditional probability and independence
6(3)
2.4 Random variables
9(2)
2.5 Expectation
11(2)
2.6 Variance
13(2)
2.7 Chebyshev's inequality and the laws of large numbers
15(2)
2.8 Some discrete random variables
17(6)
2.9 Continuous random variables
23(7)
2.10 Conditional expectation and conditional variance
30(9)
Exercises
32(5)
References
37(2)
3 Random numbers
39(8)
Introduction
39(1)
3.1 Pseudorandom number generation
39(1)
3.2 Using random numbers to evaluate integrals
40(7)
Exercises
44(1)
References
45(2)
4 Generating discrete random variables
47(22)
4.1 The inverse transform method
47(6)
4.2 Generating a Poisson random variable
53(1)
4.3 Generating binomial random variables
54(1)
4.4 The acceptance--rejection technique
55(2)
4.5 The composition approach
57(2)
4.6 The alias method for generating discrete random variables
59(3)
4.7 Generating random vectors
62(7)
Exercises
63(6)
5 Generating continuous random variables
69(30)
Introduction
69(1)
5.1 The inverse transform algorithm
69(4)
5.2 The rejection method
73(9)
5.3 The polar method for generating normal random variables
82(4)
5.4 Generating a Poisson process
86(1)
5.5 Generating a nonhomogeneous Poisson process
87(3)
5.6 Simulating a two-dimensional Poisson process
90(9)
Exercises
94(3)
References
97(2)
6 The multivariate normal distribution and copulas
99(12)
Introduction
99(1)
6.1 The multivariate normal
99(2)
6.2 Generating a multivariate normal random vector
101(3)
6.3 Copulas
104(5)
6.4 Generating variables from copula models
109(2)
Exercises
109(2)
7 The discrete event simulation approach
111(22)
Introduction
111(1)
7.1 Simulation via discrete events
111(1)
7.2 A single-server queueing system
112(3)
7.3 A queueing system with two servers in series
115(1)
7.4 A queueing system with two parallel servers
116(3)
7.5 An inventory model
119(1)
7.6 An insurance risk model
120(2)
7.7 A repair problem
122(2)
7.8 Exercising a stock option
124(2)
7.9 Verification of the simulation model
126(7)
Exercises
127(3)
References
130(3)
8 Statistical analysis of simulated data
133(18)
Introduction
133(1)
8.1 The sample mean and sample variance
133(5)
8.2 Interval estimates of a population mean
138(3)
8.3 The bootstrapping technique for estimating mean square errors
141(10)
Exercises
147(2)
References
149(2)
9 Variance reduction techniques
151(78)
Introduction
151(2)
9.1 The use of antithetic variables
153(7)
9.2 The use of control variates
160(6)
9.3 Variance reduction by conditioning
166(14)
9.4 Stratified sampling
180(10)
9.5 Applications of stratified sampling
190(9)
9.6 Importance sampling
199(13)
9.7 Using common random numbers
212(1)
9.8 Evaluating an exotic option
213(4)
9.9 Appendix: Verification of antithetic variable approach when estimating the expected value of monotone functions
217(12)
Exercises
219(8)
References
227(2)
10 Additional variance reduction techniques
229(26)
Introduction
229(1)
10.1 The conditional Bernoulli sampling method
229(4)
10.2 A simulation estimator based on an identity of Chen--Stein
233(8)
10.3 Using random hazards
241(5)
10.4 Normalized importance sampling
246(4)
10.5 Latin hypercube sampling
250(5)
Exercises
252(3)
11 Statistical validation techniques
255(24)
Introduction
255(1)
11.1 Goodness of fit tests
255(7)
11.2 Goodness of fit tests when some parameters are unspecified
262(3)
11.3 The two-sample problem
265(6)
11.4 Validating the assumption of a nonhomogeneous Poisson process
271(8)
Exercises
275(2)
References
277(2)
12 Markov chain Monte Carlo methods
279(32)
Introduction
279(1)
12.1 Markov chains
279(3)
12.2 The Hastings--Metropolis algorithm
282(2)
12.3 The Gibbs sampler
284(10)
12.4 Continuous time Markov chains and a queueing loss model
294(4)
12.5 Simulated annealing
298(2)
12.6 The sampling importance resampling algorithm
300(4)
12.7 Coupling from the past
304(7)
Exercises
306(2)
References
308(3)
Index 311
Dr. Sheldon M. Ross is a professor in the Department of Industrial and Systems Engineering at the University of Southern California. He received his PhD in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of INFORMS, and a recipient of the Humboldt US Senior Scientist Award.