Testing convexity or concavity of a cumulated hazard rate

In this paper, we build a statistical test of aging on a given period, in the increasing failure rate (IFR) or decreasing failure rate (DFR) sense. More precisely, we build a nonparametric test for the null hypothesis that a cumulated hazard rate is convex (or concave) on a given interval, against the alternative that it is not. The observations are right-censored data, and the censoring variables are possibly random with an unknown distribution. Theoretical properties of the statistical test are studied. It has asymptotic level alpha; and good asymptotic power against fixed, and local alternatives. The procedure is applied to two real data sets.