A New Extension of the Kumaraswamy Generated Family of Distributions with Applications to Real Data

In this paper, we develop the new extended Kumaraswamy generated (NEKwG) family of distributions. It aims to improve the modeling capability of the standard Kumaraswamy family by using a one-parameter exponential-logarithmic transformation. Mathematical developments of the NEKwG family are provided, such as the probability density function series representation, moments, information measure, and order statistics, along with asymptotic distribution results. Two special distributions are highlighted and discussed, namely, the new extended Kumaraswamy uniform (NEKwU) and the new extended Kumaraswamy exponential (NEKwE) distributions. They differ in support, but both have the features to generate models that accommodate versatile skewed data and non-monotone failure rates. We employ maximum likelihood, least-squares estimation, and Bayes estimation methods for parameter estimation. The performance of these methods is discussed using simulation studies. Finally, two real data applications are used to show the flexibility and importance of the NEKwU and NEKwE models in practice.