A New Distribution Family Constructed by Fractional Polynomial Rank Transmutation

In this study, a new polynomial rank transmutation is proposed with thehelp of the idea of quadratic rank transmutation mapping (qrtm). this polynomialrank 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 atransmuted distribution constructed by qrtm. the distribution family obtained in thistransmutation is considered to be an alternative to the distribution families obtainedby quadratic rank transmutation. statistical and reliability properties of this family areexamined. considering weibull distribution as the base distribution, the importanceand the flexibility of the proposed families are illustrated by two applications.