Extending an Order-Statistic Characterization of the Exponential Distribution
arXiv:2607.13302
summary
The paper establishes a new characterization of the exponential distribution using a linear combination of order statistics, extending earlier results and employing derived properties of Stirling numbers of the second kind.
Abstract
We prove a novel characterization of the exponential distribution via a linear combination of order statistics. The theorem established herein generalizes the previous characterization theorem given in Milošević and Obradović (2016a). The proof relies on properties of Stirling numbers of the second kind, which are derived for this purpose and may be of independent interest.
20 pages, 0 figures
Topics & keywords
#exponential distribution#order statistics#characterization theorems#stirling numbers#probability theoryexponential distributionorder statisticsStirling numbers of the second kindcharacterizationlinear combination