Some limit theorems for ratios of order statistics from uniform random variables

Abstract

Abstract In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large deviation principle, the Marcinkiewicz-Zygmund law of large numbers and complete convergence.

Keywords

• uniform distribution
• order statistics
• complete convergence
• large deviation principle
• almost sure central limit theorem