Simulation allows complex real world situations to be analyzed quantitatively. First, a model is created to represent the situation, then, using probability and statistics theory, the computer can perform a simulation to predict the outcome of this situation. This text provides a description of the generation of random variables and their use in analyzing a model in simulation study. It details how a computer may be used to generate random numbers, which may then be used to generate the behaviour of a stochastic model over time. The statistics needed to analyze simulated data and to validate the simulation model are also presented.
- Hardback | 304 pages
- 157.5 x 226.1 x 20.3mm | 476.28g
- 19 Nov 1996
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
- 2nd Revised edition
- b&w illustrations, references, index
Table of contents
Part 1 Elements of probability: sample space and events; axioms of probability; conditional probability and independence; random variables; expectation; variance; Chebyshev's inequality and the laws of large numbers; some discrete random variables; continuous random variables; conditional expectation and conditional variance problems. Part 2 Random numbers: pseudo-random number generation; using random numbers to evaluate integrals. Part 3 Generating discrete random variables: the inverse transform method; generating a Poisson random variable; generating binomial random variables; the acceptance-rejection technique; the composition approach. Part 4 Generating continuous random variables: the inverse transform algorithm; the rejection method; the polar method for generating normal random variables; generating a Poisson process; generating a non-homogeneous Poisson process. Part 5 The discrete event simulation approach: simulation via discrete events; a single server queueing system; a queueing system with two servers in series; a queueing system with two parallel servers; an inventory model; a repair problem; exercising a stock option; verification of the simulation model problems. Part 6 Statistical analysis of simulated data: the sample means and sample variance; interval estimates of a population mean; the bootstrapping technique for estimating mean square errors. Part 7 Variance reduction techniques: the use of antipathetic variables; the use of control variates; variance reduction by conditioning; stratified sampling; importance sampling; using common random numbers. Part 8 Statistical validation techniques: goodness of fit tests; goodness of fit tests when some parameters are unspecified; the two-sample problem; validating the assumption of a nonhomogeneous Poisson process. Part 9 Markov chain Monte Carlo methods: Markov chains; the Hastings-Metropolis algorithm; the Gibbs sampler; simulated annealing; the sampling importance; resampling algorithm. Part 10 Some additional topics: the alias method for generating discrete random variables; simulating a two-dimensional Poisson process; simulation applications of an identity for sums of Bernoulli random variables; estimating probabilities and expected first passage times by using random hazards; appendix.
..".quite useful as a reference for the applied statistician."--TECHNOMETRICS