Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 938545, 8 pages
http://dx.doi.org/10.1155/2013/938545
Research Article

Average Sample Number Function for Pareto Heavy Tailed Distributions

Department of Mathematics and Computer Science, University of Tebessa, Algeria

Received 21 April 2013; Accepted 9 May 2013

Academic Editors: S.-W. Chyuan and Q. Song

Copyright © 2013 Boukhalfa El-Hafsi. 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

The main purpose of this work is shortly to give the average sample number function after a sequential probability ratio test on the index parameter alpha of stable densities, which we give a mean of the number of data required to take decision in the case , we use the fact that the tails of Levy-stable distributions are asymptotically equivalent to a Pareto law for large data. Stable distributions are a rich class of probability distributions that allow skewness and heavy tails and have many intriguing mathematical properties. The lack of closed formulas for densities and distribution functions for all has been a major drawback to the use of stable distributions by practitioners, but few stable distributions have the analytical formula of their densities functions which are Gauss, Levy, and Cauchy.