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Research Article | Open Access

Minimum of heavy-tailed random variables is not heavy tailed

Remigijus Leipus1, Jonas Šiaulys2( ), Dimitrios Konstantinides3
Institute of Applied Mathematics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania
Institute of Mathematics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania
Department of Statistics and Actuarial-Financial Mathematics, University of Aegean, Karlovasi, GR-83 200 Samos, Greece
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Abstract

By constructing an appropriate example, we show that the class of heavy-tailed distributions is not closed under minimum. We provide two independent heavy-tailed random variables, such that their minimum is not heavy tailed. In addition, we establish a few properties of the distributions considered in the example.

Keywords

heavy-tailed distributionclosure propertiesminimum of random variablesclosure under minimumgeneralized long-tailed distribution
CLC number: 26E40, 46F10, 60E05

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13066-13072
DOI: 10.3934/math.2023658

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Cite this article:
Leipus R, Šiaulys J, Konstantinides D. Minimum of heavy-tailed random variables is not heavy tailed. AIMS Mathematics, 2023, 8(6): 13066-13072. https://doi.org/10.3934/math.2023658

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Received: 28 October 2022
Revised: 08 March 2023
Accepted: 17 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)