A Note on Classes of Lifetime Distributions

Abstract Some classes of lifetime distributions based on the failure rate are considered, namely new better than used failure rate (NBUFR), new better than average renewal failure rate (NBARFR) and generalized new better than average renewal failure rate (GNBARFR). Moment inequalities and moment generating functions of these classes under mixture and convolution are studied. In addition, the relationship between the scaled TTT-transform and the NBARFR class is investigated.