Extending an Order-Statistic Characterization of the Exponential Distribution

Danijel G. Aleksić; Dušan Džamić; Bojana Milošević; Marko Obradović

Extending an Order-Statistic Characterization of the Exponential Distribution

Probability 2026-07-14 v1

Authors: Danijel G. Aleksić , Dušan Džamić , Bojana Milošević , Marko Obradović

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 Milo\v{s}evi\'c and Obradovi\'c (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.

Keywords

exponential distribution order statistics characterization theorem Stirling numbers of the second kind linear combination

Cite

@article{arxiv.2607.13302,
  title  = {Extending an Order-Statistic Characterization of the Exponential Distribution},
  author = {Danijel G. Aleksić and Dušan Džamić and Bojana Milošević and Marko Obradović},
  journal= {arXiv preprint arXiv:2607.13302},
  year   = {2026}
}

Comments

18 pages, 0 figures