On a characterization of the exponential distribution by properties of order statistics
A continuous c.d.f. F(x), strictly increasing for \(x>0\), is exponential if and only if \(X_{j,n}-X_{i,n}\) and \(X_{j-i,n-i}\) have identical distributions for some i,n, \(j=j_ 1,j_ 2\), \(1\leq i<j_ 1<j_ 2\leq n\), \(n\geq 3\). A new proof of this characterization is given, since in \textit{M. Ahsanullah}'s paper in G. P. Patil, S. Kotz and J. K. Ord (eds.), A modern course on statistical distributions in scientific work. Vol. 3. NATO Advanced Study Institutes Series. Ser. C (1975; Zbl 0308.60003), p. 131-135, where it was stated first, an implicit assumption in the proof is that F is NBU or NWU.
scientific article; zbMATH DE number 4070020