Average sample number function for Pareto heavy tailed distributions
type: Item
instance of: scholarly article
title: Average sample number function for Pareto heavy tailed distributions
zbMATH Open document ID: 1298.60035
DOI: 10.1155/2013/938545
author: Boukhalfa El-Hafsi
published in: ISRN Applied Mathematics
publication date: 2014-11-11T00:00:00Z
review text: Summary: 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 \(1<\alpha<2\). 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 density functions which are Gauss, Levy, and Cauchy.
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 6368334
Wikidata QID: Q59001264
describes a project that uses: STABLE
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/938545
OpenAlex ID: W2157569327
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description: scientific article; zbMATH DE number 6368334