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New examples of heavy-tailed O-subexponential distributions and related closure properties

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  • Lin, Jianxi
  • Wang, Yuebao

Abstract

Let L and S denote the classes of distributions with long tails and subexponential tails respectively. Let OS denote the class of distributions with O-subexponential tails, which means the distributions with the tails having the same order as the tails of their 2-fold convolutions. In this paper, we first construct a family of distributions without finite means in L∩OS∖S. Next some distributions in L∩OS∖S, which possess finite means or even finite higher moments, are also constructed. In connection with this, we prove that the class OS is closed under minimization of random variables. However, it is not closed under maximization of random variables.

Suggested Citation

  • Lin, Jianxi & Wang, Yuebao, 2012. "New examples of heavy-tailed O-subexponential distributions and related closure properties," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 427-432.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:427-432
    DOI: 10.1016/j.spl.2011.12.011
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    References listed on IDEAS

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    1. Yu, Changjun & Wang, Yuebao & Cui, Zhaolei, 2010. "Lower limits and upper limits for tails of random sums supported on," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1111-1120, July.
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    Cited by:

    1. Jiang, Tao & Gao, Qingwu & Wang, Yuebao, 2014. "Max-sum equivalence of conditionally dependent random variables," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 60-66.

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