Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 191604, 14 pages
Research Article

A Method for Simulating Burr Type III and Type XII Distributions through -Moments and -Correlations

1Department of Curriculum and Instruction, 320-B Science Hall, University of Texas at Arlington, Arlington, TX 76019, USA
2Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, 222-J Wham Bldg, Carbondale, IL 62901-4618, USA

Received 27 January 2013; Accepted 27 March 2013

Academic Editors: F. Ding, E. Skubalska-Rafajlowicz, and F. Zirilli

Copyright © 2013 Mohan D. Pant and Todd C. Headrick. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and the -correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -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 -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 -skew, -kurtosis, and -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.