Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 209-214
Citer cet article
O. P. Vinogradov. On summing a random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 209-214. http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a24/
@article{TVP_1976_21_1_a24,
author = {O. P. Vinogradov},
title = {On summing a~random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {209--214},
year = {1976},
volume = {21},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a24/}
}
TY - JOUR
AU - O. P. Vinogradov
TI - On summing a random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1976
SP - 209
EP - 214
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a24/
LA - ru
ID - TVP_1976_21_1_a24
ER -
%0 Journal Article
%A O. P. Vinogradov
%T On summing a random number of random variables with increasing hazard rate or with strongly unimodal discrete distribution
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1976
%P 209-214
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a24/
%G ru
%F TVP_1976_21_1_a24
Let $\xi_1,\dots,\xi_n,\dots$ be independent identically distributed random variables and let $F(t)=\mathbf P\{\xi_i have an inscreasing hazard rate (IHR) [1]. The random sum $\zeta=\xi_1+\dots+\xi_{\tau}$ 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.
