Two New Distribution Families Constructed by a Modified Rank Transmutation

Abstract

In this study, two new distribution families are derived by modifying the rank transmutation. Thebase distribution of one of these two families is F2, and the other is F. The modification on the ranktransmutation allowed to extend the range of the transmutation parameter from [−1, 1] to [−1, 2]. At thispoint, the generated distributions gain more flexibility. Considering exponential distribution as the basedistribution, the importance and flexibility of the proposed families are illustrated by two applications.Since the structure of the transmuted family with base distribution is simpler, the statistical and reliabilityproperties of this family are examined. Furthermore, some orderings based on the survival and hazardrate revealed.