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E-grāmata: Simulation

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(Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USA)
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Ross's Simulation, Fourth Edition introduces 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 learn to apply results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions about future outcomes.
This text explains 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. It presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.

* Ross's writing style gives the text personality and makes the material interesting and lively
* Presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model
* Examples integrated throughout the text illustrate the theory and show applications to subjects such as multiple server queuing methods, inventory control, and exercising stock options

Recenzijas

"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 outstanding because it is what it is and no other textbook out there does this job." --Kris Ostaszewski, Illinois State University

"Examples are infinitely more interesting than in almost any other book! Ross always explains clearly, I especially enjoy the exposition of the brand new sections." --Matt Carlton, Cal Polytechnic Institute

Preface ix
1 Introduction
1(4)
Exercises
3(2)
2 Elements of Probability
5(36)
2.1 Sample Space and Events
5(1)
2.2 Axioms of Probability
6(1)
2.3 Conditional Probability and Independence
7(2)
2.4 Random Variables
9(2)
2.5 Expectation
11(3)
2.6 Variance
14(2)
2.7 Chebyshev's Inequality and the Laws of Large Numbers
16(2)
2.8 Some Discrete Random Variables
18(6)
Binomial Random Variables
18(2)
Poisson Random Variables
20(2)
Geometric Random Variables
22(1)
The Negative Binomial Random Variable
23(1)
Hypergeometric Random Variables
24(1)
2.9 Continuous Random Variables
24(9)
Uniformly Distributed Random Variables
25(1)
Normal Random Variables
26(1)
Exponential Random Variables
27(2)
The Poisson Process and Gamma Random Variables
29(3)
The Nonhomogeneous Poisson Process
32(1)
2.10 Conditional Expectation and Conditional Variance
33(2)
The Conditional Variance Formula
34(1)
Exercises
35(4)
References
39(2)
3 Random Numbers
41(8)
Introduction
41(1)
3.1 Pseudorandom Number Generation
41(1)
3.2 Using Random Numbers to Evaluate Integrals
42(4)
Exercises
46(2)
References
48(1)
4 Generating Discrete Random Variables
49(18)
4.1 The Inverse Transform Method
49(6)
4.2 Generating a Poisson Random Variable
55(2)
4.3 Generating Binomial Random Variables
57(1)
4.4 The Acceptance–Rejection Technique
58(2)
4.5 The Composition Approach
60(1)
4.6 Generating Random Vectors
61(1)
Exercises
62(5)
5 Generating Continuous Random Variables
67(26)
Introduction
67(1)
5.1 The Inverse Transform Algorithm
67(4)
5.2 The Rejection Method
71(7)
5.3 The Polar Method for Generating Normal Random Variables
78(4)
5.4 Generating a Poisson Process
82(1)
5.5 Generating a Nonhomogeneous Poisson Process
83(4)
Exercises
87(4)
References
91(2)
6 The Discrete Event Simulation Approach
93(24)
Introduction
93(1)
6.1 Simulation via Discrete Events
93(1)
6.2 A Single-Server Queueing System
94(3)
6.3 A Queueing System with Two Servers in Series
97(2)
6.4 A Queueing System with Two Parallel Servers
99(3)
6.5 An Inventory Model
102(1)
6.6 An Insurance Risk Model
103(2)
6.7 A Repair Problem
105(3)
6.8 Exercising a Stock Option
108(2)
6.9 Verification of the Simulation Model
110(1)
Exercises
111(4)
References
115(2)
7 Statistical Analysis of Simulated Data
117(20)
Introduction
117(1)
7.1 The Sample Mean and Sample Variance
117(6)
7.2 Interval Estimates of a Population Mean
123(3)
7.3 The Bootstrapping Technique for Estimating Mean Square Errors
126(7)
Exercises
133(2)
References
135(2)
8 Variance Reduction Techniques
137(82)
Introduction
137(2)
8.1 The Use of Antithetic Variables
139(8)
8.2 The Use of Control Variates
147(7)
8.3 Variance Reduction by Conditioning
154(12)
Estimating the Expected Number of Renewals by Time t
164(2)
8.4 Stratified Sampling
166(9)
8.5 Applications of Stratified Sampling
175(9)
Analyzing Systems Having Poisson Arrivals
176(4)
Computing Multidimensional Integrals of Monotone Functions
180(2)
Compound Random Vectors
182(2)
8.6 Importance Sampling
184(13)
8.7 Using Common Random Numbers
197(1)
8.8 Evaluating an Exotic Option
198(5)
8.9 Estimating Functions of Random Permutations and Random Subsets
203(4)
Random Permutations
203(3)
Random Subsets
206(1)
8.10 Appendix: Verification of Antithetic Variable Approach
When Estimating the Expected Value of Monotone Functions
207(2)
Exercises
209(8)
References
217(2)
9 Statistical Validation Techniques
219(26)
Introduction
219(1)
9.1 Goodness of Fit Tests
219(8)
The Chi-Square Goodness of Fit Test for Discrete Data
220(2)
The Kolmogorov–Smirnov Test for Continuous Data
222(5)
9.2 Goodness of Fit Tests When Some Parameters Are Unspecified
227(3)
The Discrete Data Case
227(3)
The Continuous Data Case
230(1)
9.3 The Two-Sample Problem
230(7)
9.4 Validating the Assumption of a Nonhomogeneous Poisson Process
237(4)
Exercises
241(3)
References
244(1)
10 Markov Chain Monte Carlo Methods 245(28)
Introduction
245(1)
10.1 Markov Chains
245(3)
10.2 The Hastings–Metropolis Algorithm
248(3)
10.3 The Gibbs Sampler
251(11)
10.4 Simulated Annealing
262(2)
10.5 The Sampling Importance Resampling Algorithm
264(5)
Exercises
269(3)
References
272(1)
11 Some Additional Topics 273(21)
Introduction
273(1)
11.1 The Alias Method for Generating Discrete Random Variables
273(4)
11.2 Simulating a Two-Dimensional Poisson Process
277(3)
11.3 Simulation Applications of an Identity for Sums of Bernoulli Random Variables
280(5)
11.4 Estimating the Distribution and the Mean of the First Passage Time of a Markov Chain
285(4)
11.5 Coupling from the Past
289(2)
Exercises
291(2)
References
293(1)
Index 294


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.
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