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Some properties of subexponential distributions

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Abstract

The nonnegative random variableX is said to have a subexponential distribution if we have (1-G(t))/(1-F(t))→2 ast→∞, whereF(t)=P{X≤t} andG(t) is the convolution ofF(t) with itself. Conditions on the distribution of independent nonnegative random variablesX andY such that max(X, Y) and min(X, Y) have a subexponential distribution are given.

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Russian Academy of Sciences, USSR

    A. L. Yakymiv

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  1. A. L. Yakymiv
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Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 138–144, July, 1997.

Translated by N. K. Kulman

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Yakymiv, A.L. Some properties of subexponential distributions. Math Notes 62, 116–121 (1997). https://doi.org/10.1007/BF02356073

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  • DOI: https://doi.org/10.1007/BF02356073

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