A characterization of Exponential Distribution and the Sukhatme-Renyi   Decomposition of Exponential Maxima
  A new characterization of the exponential distribution is established. It is proven that the well-known Sukhatme-Renyi necessary condition is also sufficient for exponentiality. A method of proof due to Arnold and Villasenor based on the Maclaurin series expansion of the density is utilized. 
George P. Yanev and Santanu Chakraborty
math.PR math.ST stat.TH