Numerical Issues in Estimation of Continuous Parametric Distributions

Zhang, Yiwei, Systems Engineering - School of Engineering and Applied Science, University of Virginia
Krzysztofowicz, Roman, Department of Systems and Information Engineering, University of Virginia

Continuous variates are used everywhere (almost) in stochastic modeling. This thesis addresses numerical issues arising in the process of estimating a continuous parametric distribution function. It aims to provide a guide to analysts on how to overcome some problems we have encountered. In detail, it (1) applies the uniform method for estimating a one- or two-parameter distribution function from a complete sample; (2) derives the Conditional Empirical Distribution method for estimating distribution function from a censored sample (of any type); (3) illustrates the superiority of the Conditional Empirical Distribution method over the Maximum Likelihood Estimation method; (4) determines the reason for difficulties (unbounded solutions) in optimization of Pareto distribution parameters; (5) demonstrates the fallacy of applying the goodness-of-fit tests meant for discrete distributions, such as the chi-square test, to continuous distributions.

MS (Master of Science)
goodness-of-fit, continuous distribution estimation, continuous distribution, censored sample
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