A Method for Simulating Burr Type III and Type XII Distributions through L-Moments and L-Correlations. (20th May 2013) - Pant, Mohan D.; Headrick, Todd C.
Abstract : This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L -moments and the L -correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L -skew, L -kurtosis, and L -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that L -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of L -skew, L -kurtosis, and L -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern.