The number of elements close to near-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 a away from the value of this "person," where a is a fixed integer. This is motivated by a recent paper by Balakrishnan and Stepanov who considered a continuous analogue of the problem.