Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 245986, 23 pages
Research Article

A Logistic -Moment-Based Analog for the Tukey - , , , and - System of Distributions

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

Received 19 May 2012; Accepted 20 June 2012

Academic Editors: F. Fagnola, D. Fiems, and C. Proppe

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 a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric - , (ii) log-logistic , (iii) symmetric , and (iv) asymmetric - . The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating - , , , and - distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that estimates of L-skew, L-kurtosis, and L-correlation associated with the - , , , and - distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.