A Sufficient Condition for Association of a Renewal Process

Burton, Robert M.; Waymire, Ed

Ann. Probab., Tome 14 (1986) no. 4, p. 1272-1276 / Harvested from Project Euclid

Résumé

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).

Publié le : 1986-10-14
Classification: Association, renewal process, 60K05, 60K10

@article{1176992368,
     author = {Burton, Robert M. and Waymire, Ed},
     title = {A Sufficient Condition for Association of a Renewal Process},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 1272-1276},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992368}
}

Burton, Robert M.; Waymire, Ed. A Sufficient Condition for Association of a Renewal Process. Ann. Probab., Tome 14 (1986) no. 4, pp.  1272-1276. http://gdmltest.u-ga.fr/item/1176992368/