On the Markov property of order statistics |
| |
Authors: | B.C. Arnold A. Becker U. Gather H. Zahedi |
| |
Affiliation: | Department of Statistics, University of California, Riverside, CA 92521, USA;Statistical Institute, RWTH Aachen, West Germany;Department of Mathematics, University of California, Santa Barbara, CA 93106, USA |
| |
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. |
| |
Keywords: | 60J99 62E99 Discrete order statistics Markov chain Geometric characterizations Exponential distribution Spacings |
本文献已被 ScienceDirect 等数据库收录! |
|