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Randomly stopped sums of not identically distributed heavy tailed random variables

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  • Danilenko, Svetlana
  • Šiaulys, Jonas

Abstract

Let {ξ1,ξ2,…} be a sequence of independent but not necessarily identically distributed non-negative random variables a number of which has distribution functions with dominatingly varying tails. Let η be a counting random variable independent of {ξ1,ξ2,…}. We consider conditions for random variables {ξ1,ξ2,…} and η under which distribution of the random sum ξ1+ξ2+⋯+ξη preserves dominatingly varying tail.

Suggested Citation

  • Danilenko, Svetlana & Šiaulys, Jonas, 2016. "Randomly stopped sums of not identically distributed heavy tailed random variables," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 84-93.
    • Handle: RePEc:eee:stapro:v:113:y:2016:i:c:p:84-93
    DOI: 10.1016/j.spl.2016.03.001
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    References listed on IDEAS

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    1. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
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    Cited by:

    1. Eryilmaz, Serkan, 2017. "On compound sums under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 228-234.

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