Order statistic

In statistics by size ordered realizations of a random sample from a continuous random variables are called order statistics. From a realization of the ordered sample with the values ​​thus obtained. is defined as the -th ordered statistics. Another common name for the order statistics.

Properties

The ordered statistics are stochastically dependent and not identically distributed.

Distribution of order statistics

For the distribution function of the th order statistic

Important special cases of the distribution obtained for the minimum ( ) and maximum ( ) as

Application

In the non- parametric statistics can be rank statistics or empirical distribution functions expressed in terms of order statistics. In addition, can be derived for quantiles of order statistics weakly consistent estimator. Next can be obtained by above-mentioned distribution over folds and transform sets the distribution of important metrics, such as the median or the span gain.