A Characterization Related to the Equilibrium Distribution Associated with a Polynomial Structure
-
Published:2010-03
Issue:01
Volume:47
Page:293-299
-
ISSN:0021-9002
-
Container-title:Journal of Applied Probability
-
language:en
-
Short-container-title:J. Appl. Probab.
Author:
Bar-Lev Shaul K.,Boxma Onno,Letac Gérard
Abstract
Let f be a probability density function on (a, b) ⊂ (0, ∞), and consider the class C
f
of all probability density functions of the form Pf, where P is a polynomial. Assume that if X has its density in C
f
then the equilibrium probability density x ↦ P(X > x) / E(X) also belongs to C
f
: this happens, for instance, when f(x) = Ce−λx
or f(x) = C(b − x)λ−1. We show in the present paper that these two cases are the only possibilities. This surprising result is achieved with an unusual tool in renewal theory, by using ideals of polynomials.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献