title: Limit properties for ratios of order statistics from exponentials.
abstract: In this paper, we study the limit properties of the ratio for order statistics based on samples from an exponential distribution and obtain the expression of the density functions, the existence of the moments, the strong law of large numbers for [Formula: see text] with [Formula: see text]. We also discuss other limit theorems such as the central limit theorem, the law of iterated logarithm, the moderate deviation principle, the almost sure central limit theorem for self-normalized sums of [Formula: see text] with [Formula: see text].
authors.affiliation: College of Mathematics, Jilin University, Changchun, 130012 P.R. China.
authors.forename: Yong
authors.identifier: 0000-0003-4443-812X
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: College of Mathematics, Jilin University, Changchun, 130012 P.R. China.
authors.forename: Xue
authors.initials: X
authors.lastname: Ding
keywords: central limit theorem; exponential distribution; law of iterated logarithm; order statistics; strong law of large numbers