Burton, Robert M. jun.; Waymire, Ed A sufficient condition for association of a renewal process. (English) Zbl 0608.60084 Ann. Probab. 14, 1272-1276 (1986). Let N be a renewal point process on [0,\(\infty)\) with life time density f and consider the family \({\mathcal F}\) of random variables N(A), A Borel subset of [0,\(\infty)\). The authors prove that \({\mathcal F}\) is ”associated” [see C. M. Newman, Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 361- 371 (1982; Zbl 0465.60010)] provided log f is a convex function. Interesting connections to reliability theory and to particle systems are stated. Reviewer: H.Wegmann Cited in 1 Document MSC: 60K05 Renewal theory 60K10 Applications of renewal theory (reliability, demand theory, etc.) Keywords:associated variables; failure rate; renewal point process; reliability theory; particle systems Citations:Zbl 0465.60010 PDF BibTeX XML Cite \textit{R. M. Burton jun.} and \textit{E. Waymire}, Ann. Probab. 14, 1272--1276 (1986; Zbl 0608.60084) Full Text: DOI OpenURL