Characterizations of Exponential Distribution Based on Two-Sided Random Shifts

Abstract

A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a recently developed technique including the Maclaurin series expansion of the probability density of the parent variable.

Keywords

• characterization
• exponential distribution
• order statistics
• random shifts