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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 209–214 (Mi tvp3321)

Short Communications

On summing a random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution

Moscow

Abstract: Let $\xi_1,…,\xi_n,…$ be independent identically distributed random variables and let $F(t)=\mathbf P\{\xi_i<t\}$ have an inscreasing hazard rate (IHR) [1]. The random sum $\zeta=\xi_1+…+\xi_{\tau}$ is considered where $\tau$ is independent of $\xi_i$ and the distribution of $\tau$ has also an IHR.
We find conditions under which the distribution of $\zeta$ has an IHR. The case of discrete $\xi_i$ is also considered. Analogous results for strongly unimodal discrete distributions are given.

Full text: PDF file (383 kB)

English version:
Theory of Probability and its Applications, 1976, 2:1, 205–209

Bibliographic databases:

Citation: O. P. Vinogradov, “On summing a random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 209–214; Theory Probab. Appl., 2:1 (1976), 205–209

Citation in format AMSBIB
\Bibitem{Vin76} \by O.~P.~Vinogradov \paper On summing a~random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution \jour Teor. Veroyatnost. i Primenen. \yr 1976 \vol 21 \issue 1 \pages 209--214 \mathnet{http://mi.mathnet.ru/tvp3321} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=421017} \zmath{https://zbmath.org/?q=an:0358.60043} \transl \jour Theory Probab. Appl. \yr 1976 \vol 2 \issue 1 \pages 205--209 \crossref{https://doi.org/10.1137/1121025}