Abstract
Let $\{F_m\}$ be a sequence of distribution functions and $X(r, n, m)$ be the $r$th order statistic in a sample of size $n$ from $F_m$. In this note we establish a relationship between the convergences of $F_m$ and $EX(r, n, m)$ as $m \rightarrow \infty$.
Citation
K. Aiyappan Nair. "On Complete Convergence of Distributions and Expected Values of Order Statistics." Ann. Probab. 5 (5) 826 - 827, October, 1977. https://doi.org/10.1214/aop/1176995728
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