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
Let and be the empirical distribution functions of two independent samples, each of size , in the case where the elements of the samples are independent random variables, each having the same continuous distribution function over the interval . Define a statistic by . In this paper the limits of and are determined for . The problem of finding the asymptotic behavior of the moments and the distribution of as has arisen in a study of the fluctuations of the inventory of locomotives in a randomly chosen railway depot.
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