On the Markov property of order statistics Article

Arnold, BC, Becker, A, Gather, U et al. (1984). On the Markov property of order statistics . Journal of Statistical Planning and Inference, 9(2), 147-154. 10.1016/0378-3758(84)90015-6

cited authors

  • Arnold, BC; Becker, A; Gather, U; Zahedi, H

abstract

  • The order statistics from a sample of size n≥3 from a discrete distribution form a Markov chain if and only if the parent distribution is supported by one or two points. More generally, a necessary and sufficient condition for the order statistics to form a Markov chain for (n≥3) is that there does not exist any atom x0 of the parent distribution F satisfying F(x0-)>0 and F(x0)<1. To derive this result a formula for the joint distribution of order statistics is proved, which is of an interest on its own. Many exponential characterizations implicitly assume the Markov property. The corresponding putative geometric characterizations cannot then be reasonably expected to obtain. Some illustrative geometric characterizations are discussed. © 1984.

authors

publication date

  • January 1, 1984

published in

Digital Object Identifier (DOI)

start page

  • 147

end page

  • 154

volume

  • 9

issue

  • 2