Abstract:
It is well known that if F is IFR, then it is also DMRI; however, the converse is not true, in general Kupka and Leo (1989) proved that a distribution with convex decreasing mean residual life (CDMRL) function has an Increasing Failure Rate (IFR) distribution. In this paper, we show that this condition (viz, convexity of DMRL) is not necessary for F to be IFR, It is observed that contrary to monotonic classes, in the non-monotonic classes. F is BFR does not imply that F is IDMRL. In thi paper, we derive a result that given an additional condition required for a BFR distribution to be an IDMRL distribution.
