## The Annals of Probability

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

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

Robert M. Burton, Jr. and Ed Waymire

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60K05: Renewal theory

Secondary: 60K10: Applications (reliability, demand theory, etc.)

**Keywords**

Association renewal process

#### Citation

Burton, Robert M.; Waymire, Ed. A Sufficient Condition for Association of a Renewal Process. Ann. Probab. 14 (1986), no. 4, 1272--1276. doi:10.1214/aop/1176992368. https://projecteuclid.org/euclid.aop/1176992368