On a probability problem connected with Railway traffic

[摘要] LetFn(x)andGn(x)be the empirical distribution functions of two independent samples, each of sizen, in the case where the elements of the samples are independent random variables, each having the same continuous distribution functionV(x)over the interval(0,1). Define a statisticθnbyθn/n=∫01[Fn(x)−Gn(x)]dV(x)−min0≤x≤1[Fn(x)−Gn(x)].In this paper the limits ofE{(θn/2n)r}(r=0,1,2,…)andP{θn/2n≤x}are determined forn→∞. The problem of finding the asymptotic behavior of the moments and the distribution ofθnasn→∞has arisen in a study of the fluctuations of the inventory of locomotives in a randomly chosen railway depot.

[学科分类] 应用数学