Journal of Mathematical Sciences

, Volume 238, Issue 4, pp 523–529

# Estimates for Order Statistics in Terms of Quantiles

• A. E. Litvak
• K. Tikhomirov
Article

Let X1, . . .,Xn be independent nonnegative random variables with cumulative distribution functions F1, F2, . . . , Fn satisfying certain (rather mild) conditions. We show that the median of kth smallest order statistic of the vector (X1, . . . , Xn) is equivalent to the quantile of order (k − 1/2)/n with respect to the averaged distribution $$F=\frac{1}{n}\sum \limits_{i=1}^n{F}_i$$.

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