Constant Rate Distributions on Partially Ordered Sets

TL;DR

This paper explores probability distributions with constant rate on partially ordered sets, extending reliability models, and investigates their properties, especially on discrete posets like rooted trees.

Contribution

It generalizes constant rate distributions to partially ordered sets and develops a rich theoretical framework including moments and point processes, focusing on discrete posets.

Findings

Developed theory for constant rate distributions on posets

Analyzed properties on rooted tree posets

Raised questions on existence for general discrete posets

Abstract

We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting 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.