A Characteristic Property of the Exponential Distribution
Ahsanullah, M.
Ann. Statist., Tome 5 (1977) no. 1, p. 580-582 / Harvested from Project Euclid
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Let $X$ be a nonnegative random variable with probability distribution function $F$. Suppose $X_{i,n} (i = 1,\cdots, n)$ is the $i$th smallest order statistics in a random sample of size $n$ from $F$. A necessary and sufficient condition for $F$ to be exponential is given which involves the identical distribution of the random variables $X$ and $(n - i) (X_{i+1,n} - X_{i,n})$ for some $i$ and $n$, $(1 \leqq i < n)$.
Publié le : 1977-05-14
Classification:  Exponential distribution,  characterization,  identical distribution,  order statistics,  62E10,  62G30 
@article{1176343860,
     author = {Ahsanullah, M.},
     title = {A Characteristic Property of the Exponential Distribution},
     journal = {Ann. Statist.},
     volume = {5},
     number = {1},
     year = {1977},
     pages = { 580-582},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343860}
}

Ahsanullah, M. A Characteristic Property of the Exponential Distribution. Ann. Statist., Tome 5 (1977) no. 1, pp.  580-582. http://gdmltest.u-ga.fr/item/1176343860/