Transmuted Kumaraswamy-G Family of distributions for modelling reliability data

This research introduced the new class of distributions, called the transmuted Kumaraswamy (TKw) G family for modelling life testing problems. The new extended family is obtained by using the quadratic rank transmutation map method, which possesses a bathtub shape for its hazard rate. Some special models in the new family are discussed. We studied some mathematical properties of the new family, including the ordinary moments, moment generating functions, probability weighted moment, quantile function, and formulated the pdf of rth order statistics. The TKw G-distribution parameters are estimated using the method of maximum likelihood. We illustrate the potentiality of the new family with two applications to the failure and service times of Aircraft windshield data.