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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

O. P. Vinogradov

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.

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

Bibliographic databases:

Received: 13.06.1974

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}


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