Permanent Expansions and Distributions of Order Statistics in the INID Case

Expansions of permanents are applied to derive expressions for the distribution functions of order statistics arising from n INID random variables. For this purpose, we apply two types of expansions. The first one is based on Ryser's method and it leads to a representation of the distribution function as a generalized mixture of distributions of order statistics from IID random variables. The second approach, which is based on the calculation of the permanent of a sum of two matrices, yields an expression in terms of products of both distributions of minima and maxima. It turns out that the most efficient way of calculating the distribution function is the one based on Ryser's expansion.