A New Distribution Family Constructed by Fractional Polynomial Rank Transmutation

In this study, a new polynomial rank transmutation is proposed with the help of the idea of quadratic rank transmutation mapping (QRTM). This polynomial rank transmutation is allowed to extend the range of the transmutation parameter from [−1, 1] to [−1, k]. At this point, the generated distributions gain more flexibility than a transmuted distribution constructed by QRTM. The distribution family obtained in this transmutation is considered to be an alternative to the distribution families obtained by quadratic rank transmutation. Statistical and reliability properties of this family are examined. Considering Weibull distribution as the base distribution, the importance and the flexibility of the proposed families are illustrated by two applications.