The number of elements close to near-shore-records in geometric samples

Abstract

The statistics of interest here are related to an independent sequence of geometrically distributed random variables. We look at the (n — k)th order statistic (=(k +1)st winner) and study the number of elements that fall exactly α away from the value of this person," where α is a fixed integer. This is motivated by a recent paper by Balakrishnan and Stepanov who considered a continuous analogue of the problem.

Keywords:Near-records, geometric distribution, asymptotic expansion, moments, Gum-bel distribution, Mellin transform

Quaestiones Mathematicae 29(2006), 447–470