Characterization of Exponential Distribution and Sukhatme-Renyi Decomposition of Exponential Maxima

George P. Yanev, Santanu Chakraborty

Published 2014-12-29Version 1

The exponential distribution is characterized by a distributional equation between a pair of maxima of independent and identically distributed random variables. In particular, it is proven that, under some regularity assumptions, the well-known Sukhatme-Renyi necessary condition for the maximum of exponential variables is sufficient to guarantee that the underlying distribution is exponential. An argument due to Arnold and Villasenor (2013) based on the Maclaurin series expansion of the probability density plays a crucial role in the proof of the main result.