ESTIMATES FOR ORDER STATISTICS IN TERMS OF QUANTILES

摘要

Let X-1,..., X_n be independent nonnegative random variables with cumulative distribution functions F_1, F_2,...., F_n satisfying certain (rather mild) conditions. We show that the median of kth smallest order statistic of the vector (X_1,...,X_n) is equivalent to the quantile of order (k-1/2) with respect to the averaged distribution F=1 Σ_(i=1)~n F_i. Bibliography: 12 titles.