A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications

In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is done via the maximum likelihood estimation method. In order to show the usefulness of the proposed model, some well‐established actuarial measures such as value‐at‐risk, expected‐shortfall, tail‐value‐at‐risk, tail‐variance, and tail‐variance‐premium are obtained. A simulation study is carried out to assess the performance of maximum likelihood estimates. The empirical analysis is carried out to show that our proposed model is better in performance as compared to other competitive models related to the extended Kumaraswamy model. Thus, insurance claim data and engineering related real‐life data sets are considered to prove this claim.