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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 980827, 23 pages
Research Article

A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation

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

Received 21 February 2012; Accepted 15 May 2012

Academic Editors: J. R. Fernandez, E. Skubalska-Rafajlowicz, and W. Yeih

Copyright © 2012 Todd C. Headrick and Mohan D. Pant. 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 introduces two families of distributions referred to as the symmetric κ and asymmetric - distributions. The families are based on transformations of standard logistic pseudo-random deviates. The primary focus of the theoretical development is in the contexts of L-moments and the L-correlation. Also included is the development of a method for specifying distributions with controlled degrees of L-skew, L-kurtosis, and L-correlation. The method can be applied in a variety of settings such as Monte Carlo studies, simulation, or modeling events. It is also demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when moderate-to-heavy-tailed distributions are of concern.