A Method for Simulating Burr Type III and Type XII Distributions through L-Moments and L-CorrelationsISRN Applied Mathematics (2013)
AbstractThis 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.
Publication DateSpring March 27, 2013
Citation InformationMohan D. Pant and Todd C. Headrick. "A Method for Simulating Burr Type III and Type XII Distributions through L-Moments and L-Correlations" ISRN Applied Mathematics Vol. 2013 Iss. Article ID 191604 (2013)
Available at: http://works.bepress.com/mohan_pant/2/