Abstract
Let X 1, X 2, ···, 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 identical distribution of the random variables (n − i + 1)(Xi, n − X i−1, n ) and (n − i)(X i+1, n − X i, n ) for one i and one n with 2 ≦ i ˂ n.
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