Simulation and the Monte Carlo Method
This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
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SYSTEMS MODELS SIMULATION
RANDOM NUMBER GENERATION
RANDOM VARIATE GENERATION
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acceptance-rejection method Ahrens Algorithm AR-3 Algorithm RS-1 Analysis antithetic variates apply approximation associated assume Cauchy distribution chi-square Comp confidence interval consider control variates convergence correlated defined denoted described digits efficiency equal example exponential distribution Fishman formula fx(x gamma given global maximum global optimization Go to step gradient Iglehart independent inverse transform method iteration Lavenberg length linear equations Mach machines Markov chain Math matrix Monte Carlo method normal distribution number of trials obtain optimization problem parameters point estimators probability procedure programming Proof Proposition Prove pseudorandom pseudorandom numbers queueing system random numbers random search algorithms random variables random vector regenerative method regenerative process Regenerative simulation Rubinstein sample sample-mean Monte Carlo Section sequence solution solving Statistical steady-state stochastic approximation Stochastic Processes stratified sampling Tadikamalla Theorem tion unbiased estimator uniformly distributed variance reduction variance reduction techniques Wiley York