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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 475781, 16 pages
http://dx.doi.org/10.5402/2012/475781
Research Article

An L-Moment-Based Analog for the Schmeiser-Deutsch Class of Distributions

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

Received 28 June 2012; Accepted 7 August 2012

Academic Editors: I. Doltsinis and E. Yee

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.

Abstract

This paper characterizes the conventional moment-based Schmeiser-Deutsch (S-D) class of distributions through the method of L-moments. The system can be used in a variety of settings such as simulation or modeling various processes. A procedure is also described for simulating S-D distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that the estimates of L-skew, L-kurtosis, and L-correlation associated with the S-D class of distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias—most notably when sample sizes are small.