On a characterization of the exponential distribution by order statistics

Abstract

Let X 1 , X2, …, Xn be a random sample of size n from a population with probability density function f(x), x >0, and let X 1,n < X 2,n < … < Xn,n be the associated order statistics. A characterization of the exponential distribution is shown by considering the identical distribution of the random variables nX 1,n and (n − i + 1)(X 1,n −; X i–1,n ) for one i and one n with 2 ≦ i ≦ n.