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Permanent expansions and distributions of order statistics in the inid case. (English) Zbl 1173.62006

Summary: Expansions of permanents are applied to derive expressions for the distribution functions of order statistics arising from \(n\) independent, nonidentically distributed (inid) random variables. For this purpose, we apply two types of expansions. The first one is based on H. J. Ryser’s method [Combinatorial mathematics. 4th ed., Carus Math. Monogr. 14 (1973; Zbl 0302.05001)] and leads to a representation of the distribution function as a generalized mixture of distributions of order statistics from independent, identically distributed (iid) random variables. The second approach, which is based on the calculation of the permanents 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.

MSC:

62E15 Exact distribution theory in statistics
62G30 Order statistics; empirical distribution functions
15A15 Determinants, permanents, traces, other special matrix functions

Citations:

Zbl 0302.05001
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References:

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