Numerical Issues in Estimation of Continuous Parametric Distributions

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.