## The Annals of Probability

### A Sufficient Condition for Association of a Renewal Process

#### Abstract

Let $\{N(t): t \geq 0\}$ be a renewal counting process with lifetime density $f(t)$. For each bounded Borel set $A$ contained in $\lbrack 0, \infty)$, denote the number of renewals in $A$ by $N(A)$. The renewal process is called associated if the corresponding family of random variables, $N(A)$, is associated. The result of this note is that the renewal process is associated whenever $\log(f)$ is a convex function (which implies a decreasing failure rate).

#### Article information

Source
Ann. Probab., Volume 14, Number 4 (1986), 1272-1276.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992368

Digital Object Identifier
doi:10.1214/aop/1176992368

Mathematical Reviews number (MathSciNet)
MR866348

Zentralblatt MATH identifier
0608.60084

JSTOR