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Domains of attraction for positive and discrete tempered stable distributions

Part of: Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  28 March 2018

Michael Grabchak
Michael Grabchak*
Affiliation:
University of North Carolina at Charlotte
*
* Postal address: Department of Mathematics and Statistics, The University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223-0001, USA. Email address: mgrabcha@uncc.edu
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Abstract

We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distributions. Our results suggest that these are natural models for sums of independent and identically distributed random variables with tempered heavy tails, i.e. tails that appear to be heavy up to a point, but ultimately decay faster.

Keywords

Discrete tempered stable distributionpositive tempered stable distributiondomain of attraction

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60E07: Infinitely divisible distributions; stable distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 30 - 42
Copyright
Copyright © Applied Probability Trust 2018 

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