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Mat. Zametki, 1997, Volume 62, Issue 1, Pages 138–144 (Mi mz1597)  

This article is cited in 5 scientific papers (total in 5 papers)

Some properties of subexponential distributions

A. L. Yakymiv

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The nonnegative random variable $X$ is said to have a subexponential distribution if we have $(1-G(t))/(1-F(t))\to2$ as $t\to\infty$, where $F(t)=\mathsf P\{X\le t\}$ and $G(t)$ is the convolution of $F(t)$ with itself. Conditions on the distribution of independent nonnegative random variables $X$ and $Y$ such that $\max(X,Y)$ and $\min(X,Y)$ have a subexponential distribution are given.

DOI: https://doi.org/10.4213/mzm1597

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English version:
Mathematical Notes, 1997, 62:1, 116–121

Bibliographic databases:

UDC: 519.2
Received: 02.11.1995

Citation: A. L. Yakymiv, “Some properties of subexponential distributions”, Mat. Zametki, 62:1 (1997), 138–144; Math. Notes, 62:1 (1997), 116–121

Citation in format AMSBIB
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\by A.~L.~Yakymiv
\paper Some properties of subexponential distributions
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 1
\pages 138--144
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619933}
\zmath{https://zbmath.org/?q=an:0923.60016}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 1
\pages 116--121
\crossref{https://doi.org/10.1007/BF02356073}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Baltrūnas, “On the Subexponential Property of a Class of Random Variables”, Math. Notes, 69:4 (2001), 571–574  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Geluk, J, “Some closure properties for subexponential distributions”, Statistics & Probability Letters, 79:8 (2009), 1108  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Wang Y. Yin Ch., “Minimum of Dependent Random Variables with Convolution-Equivalent Distributions”, Commun. Stat.-Theory Methods, 40:18 (2011), 3245–3251  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Beck S., Blath J., Scheutzow M., “a New Class of Large Claim Size Distributions: Definition, Properties, and Ruin Theory”, Bernoulli, 21:4 (2015), 2457–2483  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Leipus R., Siaulys J., “On a Closure Property of Convolution Equivalent Class of Distributions”, J. Math. Anal. Appl., 490:1 (2020), 124226  crossref  isi
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