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A Method for Simulating Burr Type III and Type XII Distributions through L-Moments and L-Correlations
ISRN Applied Mathematics (2013)
  • Mohan D. Pant, University of Texas at Arlington
  • Todd C. Headrick, Southern Illinois University Carbondale
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.
Publication Date
Spring March 27, 2013
Citation Information
Mohan 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/