Some new characterization results on exponential and related distributions

Abstract

It is well-known that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. Here, we consider the functional equation F(x) = F(xy) + F(xQ(y)), x, xQ(y) ∈ [0, θ), y ∈ [0, 1], where F and Q satisfy certain conditions, to give some new characterization results on exponential, power and Pareto distributions using the concepts of conditional random variables and order statistics. © 2010 Iranian Mathematical Society.