Let be independent and identically distributed random variables subject to a continuous distribution function , let be the corresponding order statistics, and write
where and are fixed integers with . It is an old question if condition (0) implies that is of exponential type. In  we showed among others that condition (0) can be greatly relaxed; namely, it can be replaced by asymptotic relations (either as or ) to derive this very result. Using a theorem on integrated Cauchy functional equations and in essential way a result of  we find now a more elegant and deeper theorem on this subject. The case of lattice distributions is also considered and some new problems are stated.
Cite this article
H.-J. Rossberg, M. Riedel, B. B. Ramachandran, Characterization of the Exponential Distribution by Properties of the Difference of Order Statistics. Z. Anal. Anwend. 16 (1997), no. 1, pp. 191–200DOI 10.4171/ZAA/758