This article is cited in 6 papers

Variational series for the scheme of summing independent variables

G. I. Ivchenko

Moscow

Abstract: Let $\xi_1,\dots,\xi_N$ be $N$ independent observations of a random variable $\xi$ and $\xi_{(m)}$ be the $m$th order statistic of this sample. We study the asymptotic behaviour of $\xi_{(m)}$ and $\xi_{(N-m+1)}$ when the distribution of $\xi$ is a convolution of $n$ identical distributions and $n,N\to\infty$.

Received: 09.02.1972

 English version: Theory of Probability and its Applications, 1974, 18:3, 531–545

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