用分位数表示的顺序统计量的估计
Estimates for order statistics in terms of quantiles
摘要：
设$X_1, \ldots, X_n$是具有累积分布函数$F_1,F_2,\ldots,F_n$的独立非负随机变量，每个累积分布函数满足一定的（相当温和的）条件。证明了向量$(X_1, \ldots, X_n)$的$k$ -th最小顺序统计量的中位数等价于$(k-1/2)/n$顺序关于平均分布$F=\frac{1}{n}\sum_{i=1}^n F_i$的分位数.
英文摘要：
Let $X_1, \ldots, X_n$ be independent non-negative random variables with cumulative distribution functions $F_1,F_2,\ldots,F_n$, each satisfying certain (rather mild) conditions. We show that the median of $k$-th smallest order statistic of the vector $(X_1, \ldots, X_n)$ is equivalent to the quantile of order $(k-1/2)/n$ with respect to the averaged distribution $F=\frac{1}{n}\sum_{i=1}^n F_i$.
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