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On Some Properties of the Discrete NBU Class Based On Generating Function Order

A new discrete class of life distributions is studied. This class is defined based on comparing the residual life time to the whole life in the probability generating function order giving “the discrete new better than used in the probability generating function order ageing class (d−NBUpg)”. Fundamental properties of this class are given including some closure properties and characterizations. Finally, we consider new results about comparisons of age and block replacement policies when the underlying distribution belongs to (d − NBUpg) aging classes.