Minimum of heavy-tailed random variables is not heavy tailed

Remigijus Leipus; Jonas Šiaulys; Dimitrios Konstantinides; Remigijus Leipus; Jonas Šiaulys; Dimitrios Konstantinides

doi:10.3934/math.2023658

AIMS Mathematics

2023, Volume 8, Issue 6: 13066-13072. doi: 10.3934/math.2023658

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Research article

Minimum of heavy-tailed random variables is not heavy tailed

1.
Institute of Applied Mathematics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania
2.
Institute of Mathematics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania
3.
Department of Statistics and Actuarial-Financial Mathematics, University of Aegean, Karlovasi, GR-83 200 Samos, Greece

Received: 28 October 2022 Revised: 08 March 2023 Accepted: 17 March 2023 Published: 03 April 2023
MSC : 26E40, 46F10, 60E05

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.
- heavy-tailed distribution,
- closure properties,
- minimum of random variables,
- closure under minimum,
- generalized long-tailed distribution
Citation: Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides. Minimum of heavy-tailed random variables is not heavy tailed[J]. AIMS Mathematics, 2023, 8(6): 13066-13072. doi: 10.3934/math.2023658

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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.

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