Abstract
Abstract This paper provided some properties of a new class of life distributions that are denoted as used better than aged in an increasing concave ordering class (UBAC(2)). This class includes many classes of life distributions like used better than aged (UBA), used better than aged in convex ordering (UBAC), used better than aged in expectation (UBAE) and decreasing mean residual life (DMRL). The considered properties included the moment inequalities, moment generating function behavior, and testing hypotheses about the survival function of this class. The distribution of the proposed statistic was investigated via simulation. We used real data as an application of the proposed test statistic.
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