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.