Order statistics of variables with given marginal distributions
Tomasz Rychlik · Lecture notes-monograph series · 1996
We review some results on order statistics based on random variables with given one-dimensional distributions.We present bounds on the distribution function of each order statistic and conditions on the marginals for attaining the bounds.For identically distributed samples, we show sharp bounds for the expectation and variance of arbitrary function of a given order statistic and for the expectation of an arbitrary X-estimate.