On a probability problem connected with Railway traffic
Lajos Takács · International Journal of Stochastic Analysis · 1991
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 urn:x-wiley:20903332:media:ista363025:ista363025-math-0001 . In this paper the limits of (r = 0, 1, 2, …) and 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.