New characterization of discrete distributions through weak records
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 4, pp. 874-880
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Let $X_{1},X_{2},\ldots$ be a sequence of independent and identically distributed random variables taking on values $0,1,\ldots$ with a distribution function $F$ such that $F(n) < 1$ for any $n=0,1,\ldots$ and $\mathbf{E} X_{1}\log (1+X_{1}) < \infty $. Let $X_{L(n)}$ be the $n$th weak record value and $\{ A_{k}\}_{k=0}^{\infty }$ be any sequence of positive numbers, such that $A_{k+1} > A_{k}-1$. This paper shows that if there exists an $F(x)$, with $\mathbf{E} \{X_{L(n+2)}-X_{L(n)}\mid X_{L(n)}=s\}=A_{s}$ for some $n > 0$ and all $s\ge 0$, then $F(x)$ is unique.
Keywords:
records, weak records, characterization of discrete distributions.
@article{TVP_1999_44_4_a10,
author = {F. A. Aliev},
title = {New characterization of discrete distributions through weak records},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {874--880},
year = {1999},
volume = {44},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_4_a10/}
}
F. A. Aliev. New characterization of discrete distributions through weak records. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 4, pp. 874-880. http://geodesic.mathdoc.fr/item/TVP_1999_44_4_a10/