The Extended Kumaraswamy Generated Family: Properties, Inference and Applications in Applied Fields

In this paper, a new Kumaraswamy generalized family is proposed. The special sub-models of the family accommodate symmetrical, left-skewed, bimodal, right-skewed unimodal, and reverse-J densities, as well as increasing, modified bathtub, decreasing, bathtub, upside down bathtub, reverse J and J shaped hazard rates. The fundamental properties of the family are derived. The maximum likelihood method and seven other methods are used for estimating the model parameters. Numerical simulations are performed to explore the performance of these estimation methods. Three real-life data sets from medicine, agriculture and engineering are fitted to illustrate the flexibility of the proposed family. The proposed family is a good alternative to the Kumaraswamy-G, beta-G, and Topp-Leone-G families.