Journal of Probability and Statistics
Volume 2013 (2013), Article ID 432642, 15 pages
Research Article

On the Generalized Lognormal Distribution

Technological Educational Institute of Athens, Department of Mathematics, Ag. Spyridonos & Palikaridi Street, 12210 Egaleo, Athens, Greece

Received 11 April 2013; Revised 4 June 2013; Accepted 5 June 2013

Academic Editor: Mohammad Fraiwan Al-Saleh

Copyright © 2013 Thomas L. Toulias and Christos P. Kitsos. 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, investigates, and discusses the -order generalized lognormal distribution ( -GLD). Under certain values of the extra shape parameter , the usual lognormal, log-Laplace, and log-uniform distribution, are obtained, as well as the degenerate Dirac distribution. The shape of all the members of the -GLD family is extensively discussed. The cumulative distribution function is evaluated through the generalized error function, while series expansion forms are derived. Moreover, the moments for the -GLD are also studied.