Geodesic
Estimates for order statistics in terms of quantiles
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 265-275 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $X_1,\dots, X_n$ be independent non-negative random variables with cumulative distribution functions $F_1,F_2,\dots,F_n$, each satisfying certain (rather mild) conditions. We show that the median of $k$-th smallest order statistic of the vector $(X_1,\dots,X_n)$ is equivalent to the quantile of order $(k-1/2)/n$ with respect to the averaged distribution $F=\frac1n\sum_{i=1}^n F_i$. 
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A. E. Litvak; K. Tikhomirov. Estimates for order statistics in terms of quantiles. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 265-275. http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a13/

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