Fast computation by block permanents of cumulative distribution functions of order statistics from several populations

TL;DR

This paper presents a more efficient method for computing the joint cumulative distribution functions of order statistics from multiple populations, significantly reducing computational complexity in certain cases.

Contribution

It introduces a fast computation technique using block permanents for the joint distribution functions of order statistics from multiple populations.

Findings

Computational cost is exponential for two populations but improved over previous methods.

Polynomial complexity achieved when only a subset of order statistics is needed.

Method significantly reduces computation time for practical applications.

Abstract

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.