On a probability problem connected with Railway traffic

Author:

Takács Lajos12

Affiliation:

1. Case Western Reserve University, Cleveland, Ohio, USA

2. 2410 Newbury Drive, Cleveland Heights, 44118, OH, USA

Abstract

Let Fn(x) and Gn(x) be the empirical distribution functions of two independent samples, each of size n, in the case where the elements of the samples are independent random variables, each having the same continuous distribution function V(x) over the interval (0,1). Define a statistic θn by θn/n=01[Fn(x)Gn(x)]dV(x)min0x1[Fn(x)Gn(x)]. In this paper the limits of E{(θn/2n)r}(r=0,1,2,) and P{θn/2nx} are determined for n. The problem of finding the asymptotic behavior of the moments and the distribution of θn as n has arisen in a study of the fluctuations of the inventory of locomotives in a randomly chosen railway depot.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Modeling and Simulation,Statistics and Probability

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