An algorithm with applications in ranked-set sampling

A mixture of order statistics is a random variable whose distribution is a finite mixture of the distributions for order statistics. Such mixtures show up in the literature on ranked-set sampling and related sampling schemes as models for imperfect rankings. In this paper, we derive an algorithm for computing the probability that independent mixtures of order statistics come in a particular order. The algorithm is far faster than previous proposals from the literature. As an application, we show that the algorithm can be used to create Kolmogorov-Smirnov-type confidence bands that adjust for the presence of imperfect rankings.