On a probability problem connected with Railway traffic. (1991)

• Record Type: Journal Article
• Authors: Takács, Lajos
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 4:Number 1(1991)
• Page Start: 1
• Page End: 27
• Publication Date: 1991
• Subjects: storage problem -- Bernoulli excursion -- limit theorems; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953391000011
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Let F n ( x ) and G n ( 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 θ n by θ n / n = ∫ 0 1 [ F n ( x ) − G n ( x ) ] d V ( x ) − min 0 ≤ x ≤ 1 [ F n ( x ) − G n ( x ) ] . In this paper the limits of E { ( θ n / 2 n ) r } ( r = 0, 1, 2, … ) and P { θ n / 2 n ≤ x } are determined for n → ∞ . The problem of finding the asymptotic behavior of the moments and the distribution of θ n as n → ∞ has arisen in a study of the fluctuations of the inventory of locomotives in a randomly chosen railway depot.