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Some closure properties for subexponential distributions

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  • Geluk, Jaap

Abstract

Let X,Y be independent random variables with subexponential distributions. In this note we show that min(X,Y) has a subexponential distribution, but this is not necessarily true for max(X,Y). We also show that Xa has a subexponential distribution when a>1.

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  • Geluk, Jaap, 2009. "Some closure properties for subexponential distributions," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1108-1111, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:8:p:1108-1111
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    Cited by:

    1. Li, Jinzhu & Tang, Qihe, 2010. "A note on max-sum equivalence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1720-1723, December.
    2. Geluk, J.L. & Frenk, J.B.G., 2011. "Renewal theory for random variables with a heavy tailed distribution and finite variance," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 77-82, January.

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