International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1991 / Article

Open Access

Volume 4 |Article ID 363025 | https://doi.org/10.1155/S1048953391000011

Lajos Takács, "On a probability problem connected with Railway traffic", International Journal of Stochastic Analysis, vol. 4, Article ID 363025, 27 pages, 1991. https://doi.org/10.1155/S1048953391000011

On a probability problem connected with Railway traffic

Received01 Dec 1990
Revised01 Jan 1991

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.

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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