SOME NEW CHARACTERIZATION RESULTS ON EXPONENTIAL AND RELATED DISTRIBUTIONS

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) is an element of [0, theta), y is an element of [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.