Journal of Probability and Statistics
Volume 2010 (2010), Article ID 675754, 21 pages
Research Article

Constant Rate Distributions on Partially Ordered Sets

Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA

Received 5 April 2010; Revised 2 August 2010; Accepted 30 August 2010

Academic Editor: Rongling Wu

Copyright © 2010 Kyle Siegrist. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting ([0,),) that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment results and results concerning ladder variables and point processes. We concentrate mostly on discrete posets, particularly posets whose graphs are rooted trees. We pose some questions on the existence of constant rate distributions for general discrete posets.