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The heavy-tail behavior of the difference of two dependent random variables

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  • Chen, Yiqing

Abstract

Consider Z=X−Y, the difference of two nonnegative dependent random variables. We investigate how the difference Z inherits the heavy tail property of the minuend X and is altered by the subtrahend Y. In the case where X and Y are tail independent, we prove that if X has a long tail F¯X=1−FX, the asymptotic behavior of F¯X is exactly inherited by Z, that is, F¯Z∼F¯X, regardless of the tail behavior of Y. However, this result may not hold when X and Y exhibit tail dependence. Within the framework of bivariate regular variation, we show that the limit of the ratio F¯ZF¯X can range over the closed interval [0,1].

Suggested Citation

  • Chen, Yiqing, 2025. "The heavy-tail behavior of the difference of two dependent random variables," Statistics & Probability Letters, Elsevier, vol. 218(C).
    • Handle: RePEc:eee:stapro:v:218:y:2025:i:c:s0167715224002761
    DOI: 10.1016/j.spl.2024.110307
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