Kernal Density Functions To Estimate Parameters To Simulate Stochastic Variables With Sparse Data: What Is The Best Distribution?
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J. W. Richardson, J. L. Outlaw & K. Schumann
The purpose of this paper was to compare the goodness-of-fit for several parametric and kernal-based distributions to determine which distribution would perform well for simulating continuous random input variables whose underlying distributions were unknown. A Monte Carlo simulation procedure was developed to estimate how well some proxy distributions performed at approximating the distributions of random input variables. We conclude that without any a priori information on which to pick a probability distribution, the distribution for simulating a random input variable with limited specifications was a Parzen kernal distribution. Keywords: probability distribution selection, kernal distributions, simulation, Simetar©. 1 What is the best probability distribution to simulate random input variables? Risk analysts who use Monte Carlo simulation techniques must specify (or assume) a probability density function (PDF) for each random input variable in their models. The question of which PDF (normal, beta, gamma, Weibull, etc.) should be used is often suggested by familiarity with the data generation process or the type of problem being analyzed (Law and Kelton [1, pp. 155-216]). Alternatively, some researchers simply assume the random input variables follow a normal distribution due to the ease of parameter estimation for this distribution and rely on the Central Limit Theorem as a justification. Another option is to estimate parameters for several proxy parametric distributions and
probability distribution selection, kernal distributions, simulation, Simetar©