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From light tails to heavy tails through multiplier

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Abstract

Let X and Y be two independent nonnegative random variables, of which X has a distribution belonging to the class \(\mathcal{L}(\gamma)\) or \(\mathcal{S}(\gamma)\) for some γ ≥ 0 and Y is unbounded. We study how their product XY inherits the tail behavior of X. Under some mild technical assumptions we prove that the distribution of XY belongs to the class \(\mathcal{L}(0)\) or \(\mathcal{S}(0)\) accordingly. Hence, the multiplier Y builds a bridge between light tails and heavy tails.

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Article 01 October 2018

Edward Omey, Stefan Van Gulck & Rein Vesilo

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA, 52242, USA

    Qihe Tang

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  1. Qihe Tang
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Correspondence to Qihe Tang.

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Tang, Q. From light tails to heavy tails through multiplier. Extremes 11, 379–391 (2008). https://doi.org/10.1007/s10687-008-0063-5

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  • DOI: https://doi.org/10.1007/s10687-008-0063-5

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