Let X be a random variable with continuous distribution nmction F(x) on the interval [0,∞), and let X 1:n ≤ X 2:n ≤ ... ≤ X n:n be the order statistics of a random sample of size n (≥ 2) from F(x). If F(x) is continuous and strictly increasing for all x > 0, then for any i and j, 1 ≤ i < j ≤ n, X j:n – X j-i:n-i have identical distribution characterize the exponential distribution. This characteristic property improve the result of Ahsanullah . In addition, the characterization is preserved if F(x) is absolutely continuous and “have identical distribution” is weakened to “have identical fmite expectation”.
Journal of Interdisciplinary Mathematics 1(1), pp.93-100