On the NBAFR (NWAFR) class of life distributions

Recently Loh (1984) presented a new generalization of the NBU class of life distributions called New Better than Average Failure Rate (NBAFR). In this paper several properties of this class are presented. For instance the closure property of its dual (NWAFR) under the operation of mixture is obtained and characterization of the NBAFR (NWAFR) property by using the Laplace transform and its relation to the cumulative damage model is studied. Some shock models which give rise to the NBAFR (NWAFR) class are discussed. Finally, a test statistic for testing exponentiality against the NBAFR alternatives is presented.