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Asymptotic behavior of product of two heavy-tailed dependent random variables

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Abstract

Let X and Y be positive weakly negatively dependent (WND) random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on \(\bar F\)(x) = 1−F(x) and \(\bar G\)(x) = 1−G(x) are provided. Moreover, subexponentiality of XY when X and Y are WND random variables is derived.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Sciences, Golestan University, P.O. Box 49138-15759, Gorgan, Iran

    Vahid Ranjbar

  2. Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

    Mohammad Amini & Abolghasem Bozorgnia

  3. Department of Mathematics, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

    Jaap Geluk

Authors
  1. Vahid Ranjbar
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  2. Mohammad Amini
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  3. Jaap Geluk
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  4. Abolghasem Bozorgnia
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Correspondence to Vahid Ranjbar.

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Supported by Ferdowsi University of Mashhad (Grant No. MS88076AMI)

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Ranjbar, V., Amini, M., Geluk, J. et al. Asymptotic behavior of product of two heavy-tailed dependent random variables. Acta. Math. Sin.-English Ser. 29, 355–364 (2013). https://doi.org/10.1007/s10114-012-0680-4

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  • DOI: https://doi.org/10.1007/s10114-012-0680-4

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