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The tail probability of the product of dependent random variables from max-domains of attraction

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  • Yang, Yingying
  • Hu, Shuhe
  • Wu, Tao

Abstract

In this article, we investigate the tail probability of the product of finitely many non-negative dependent random variables. They follow distributions from max-domains of attraction of extreme value distributions and their dependence is modeled via a multivariate Farlie–Gumbel–Morgenstern distribution. For each of the Fréchet, Gumbel and Weibull cases, we obtain an explicit asymptotic formula for the tail probability of the product. Our study extends a few known results in the literature.

Suggested Citation

  • Yang, Yingying & Hu, Shuhe & Wu, Tao, 2011. "The tail probability of the product of dependent random variables from max-domains of attraction," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1876-1882.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1876-1882
    DOI: 10.1016/j.spl.2011.06.018
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    References listed on IDEAS

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    Cited by:

    1. Qu, Zhihui & Chen, Yu, 2013. "Approximations of the tail probability of the product of dependent extremal random variables and applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 169-178.
    2. Fontanari, Andrea & Taleb, Nassim Nicholas & Cirillo, Pasquale, 2018. "Gini estimation under infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 256-269.
    3. Chen, Yiqing & Liu, Jiajun & Liu, Fei, 2015. "Ruin with insurance and financial risks following the least risky FGM dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 98-106.
    4. Yang, Yang & Hashorva, Enkelejd, 2013. "Extremes and products of multivariate AC-product risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 312-319.
    5. Nassim Nicholas Taleb, 2020. "Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications," Papers 2001.10488, arXiv.org, revised Nov 2022.

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