401 – Monte Carlo Methods

A Characterization of Burr Type III and Type XII Distributions Through the Method of Percentiles

at Southern Illinois University at Carbondale

Burr Type III and Type XII distributions have been mainly used in statistical modeling of events in a variety of applied mathematical contexts such as fracture roughness, life testing, meteorology, modeling crop prices, forestry, reliability analysis, and in the context of Monte Carlo simulation studies. A preponderance of the applications associated with the Burr Type III and Type XII distributions are based on the method of moments (MOM). However, estimators of conventional skew and kurtosis can be substantially (a) biased, (b) dispersed, or (c) influenced by outliers. To obviate these problems, a characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the MOM in the context of estimation and fitting theoretical and empirical distributions. The methodology is based on simulating Burr Type III and Type XII distributions with specified values of medians, inter-decile ranges, left-right tail-weight ratios (a skew function), and tail-weight factors (a kurtosis function). Evaluation of the proposed procedure demonstrates that the estimates of left-right tail-weight ratios and tail-weight factors are substantially superior to their MOM-based counterparts of skew and kurtosis in terms of relative bias and relative efficiency-most notably when heavy-tailed distributions are of concern.