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Weak max-sum equivalence for dependent heavy-tailed random variables

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Abstract

We consider real-valued random variables X 1,…,X n with corresponding distributions F 1,…, F n such that X 1,…,X n admit some dependence structure and n −1(F 1 +· · ·+F n ) belongs to the class of dominatedly varyingtailed distributions. We establish weak equivalence relations among P(S n > x), P(max{X 1,…,X n } > x), P(max{S 1,…,S n } > x), and \( {\displaystyle {\sum}_{k=1}^n\overline{F_k}(x)} \) as x → ∞, where S k := X 1 + · · · + X k . Some copula-based examples illustrate the results.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Lina Dindienė & Remigijus Leipus

  2. Institute of Mathematics and Informatics, Vilnius University, Akademijos str. 4, LT-08663, Vilnius, Lithuania

    Remigijus Leipus

Authors
  1. Lina Dindienė
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  2. Remigijus Leipus
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Correspondence to Lina Dindienė.

Additional information

The author is supported by a grant (No. MIP-13079) from the Research Council of Lithuania.

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Dindienė, L., Leipus, R. Weak max-sum equivalence for dependent heavy-tailed random variables. Lith Math J 56, 49–59 (2016). https://doi.org/10.1007/s10986-016-9303-6

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  • DOI: https://doi.org/10.1007/s10986-016-9303-6

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