Characterizations of the exponential distribution by higher-order gap |
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Authors: | M. Ahsanullah |
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Abstract: | Suppose X1,X2, ?,Xn is a random sample of size n from a continuous distribution function F(x) and let X1,n, ≦ X2,n ≦ ? ≦ Xn,n be the corresponding order statistics. We define the jth-order gap gi,j as gi,j = Xi+j,n ? Xi,n, 1 ≦ i < n, 1 ≦ j ≦ n ? i. In this article characterizations of the exponential distribution are given by considering the distributional properties of gk,n-k, 1 ≦ k ≦ n. |
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