Characterization of the Exponential Distribution by Properties of the Difference of Order Statistics

  • H.-J. Rossberg

    Universität Leipzig, Germany
  • M. Riedel

    Universität Leipzig, Germany
  • B. B. Ramachandran

    New Delhi, India

Abstract

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 [8] 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 [8] 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. 191–200

DOI 10.4171/ZAA/758