Lower limits for distribution tails of randomly stopped sums

D.E. Denisov; D.A. Korshunov; S.G. Foss

doi:10.1137/S0040585X97983328

Lower limits for distribution tails of randomly stopped sums

D.E. Denisov
, D.A. Korshunov
, S.G. Foss

Eurandom

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

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Abstract

We study lower limits for the ratio $\overline{F^{*\tau}}(x)/\,\overline F(x)$ of tail distributions, where $F^{*\tau}$ is a distribution of a sum of a random size $\tau$ of independent identically distributed random variables having a common distribution $F$, and a random variable $\tau$ does not depend on the summands.

Original language	English
Pages (from-to)	690-699
Journal	Theory of Probability and Its Applications
Volume	52
Issue number	4
DOIs	https://doi.org/10.1137/S0040585X97983328
Publication status	Published - 2008

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title = "Lower limits for distribution tails of randomly stopped sums",

abstract = "We study lower limits for the ratio \$\textbackslash{}overline\{F\textasciicircum{}\{*\textbackslash{}tau\}\}(x)/\textbackslash{},\textbackslash{}overline F(x)\$ of tail distributions, where \$F\textasciicircum{}\{*\textbackslash{}tau\}\$ is a distribution of a sum of a random size \$\textbackslash{}tau\$ of independent identically distributed random variables having a common distribution \$F\$, and a random variable \$\textbackslash{}tau\$ does not depend on the summands.",

author = "D.E. Denisov and D.A. Korshunov and S.G. Foss",

year = "2008",

doi = "10.1137/S0040585X97983328",

language = "English",

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pages = "690--699",

journal = "Theory of Probability and Its Applications",

issn = "0040-585X",

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T1 - Lower limits for distribution tails of randomly stopped sums

AU - Denisov, D.E.

AU - Korshunov, D.A.

AU - Foss, S.G.

PY - 2008

Y1 - 2008

N2 - We study lower limits for the ratio $\overline{F^{*\tau}}(x)/\,\overline F(x)$ of tail distributions, where $F^{*\tau}$ is a distribution of a sum of a random size $\tau$ of independent identically distributed random variables having a common distribution $F$, and a random variable $\tau$ does not depend on the summands.

AB - We study lower limits for the ratio $\overline{F^{*\tau}}(x)/\,\overline F(x)$ of tail distributions, where $F^{*\tau}$ is a distribution of a sum of a random size $\tau$ of independent identically distributed random variables having a common distribution $F$, and a random variable $\tau$ does not depend on the summands.

U2 - 10.1137/S0040585X97983328

DO - 10.1137/S0040585X97983328

M3 - Article

SN - 0040-585X

VL - 52

SP - 690

EP - 699

JO - Theory of Probability and Its Applications

JF - Theory of Probability and Its Applications

IS - 4

ER -

Lower limits for distribution tails of randomly stopped sums

Abstract

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