An Automated Procedure for Stochastic Simulation Input Modeling with Bezier Distributions

Abstract

As a means of handling the problem of input modeling forstochastic simulation experiments, we build upon previous workof Wagner and Wilson using Bézier distributions. Wagner andWilson proposed a likelihood ratio test to determine how manycontrol points (that is, parameters) a Bézier distributionshould have to adequately model sample data. In this thesis, weextend this input-modeling methodology in two directions. First,we establish the asymptotic properties of the Likelihood RatioTest (LRT) as the sample size tends to infinity. The asymptoticanalysis applies only to maximum likelihood estimation withknown endpoints and not to any other parameter estimationprocedure, nor to situations in which the endpoints of thetarget distribution are unknown. Second, we perform acomprehensive Monte Carlo evaluation of this procedure forfitting data together with other estimation procedures based onleast squares and minimum L norm estimation. In the MonteCarlo performance evaluation, several different goodness-of-fitmeasures are formulated and used to evaluate how well the fittedcumulative distribution function (CDF) compares to theempirical CDF and to the actual CDF from which the samplescame. The Monte Carlo experiments show that in addition toworking well with the method of maximum likelihood when theendpoints of the target distribution are known, the LRT alsoworks well with minimum L norm estimation and least squaresestimation; moreover, the LRT works well with suitablyconstrained versions of these three estimation methods when theendpoints are unknown and must also be estimated.