Generalizations of the theorems of smirnov with application to a reliability type inventory problem

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Abstract
Let r be the number of elements of a sample taken from a population uniformly distributed in [0,1]. Let α ≥ 0 be a number such that λ=n α ≤ 1. Subdivide an interval of length 1 - λ into n parts by n - 1 independently and uniformly distributed points. Denote the lengths of these subintervals. Using the notations the generalizations of the theorems of SMIRNOV are expressed by (4.14), (4.15), where Gm(t, μ) is defined similarly to Fn(t, λ) and these two stochastic processes are aupposec! to be independent. These theorems were already published in [7] the proofs are given here. Applications to inventory problems are also mentioned.

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