Kumaraswamy Alpha Power Lomax Distribution: Properties and Applications in Actuarial Sciences

The Kumaraswamy alpha power Lomax model, a five-parameter sub-model of the Kumaraswamy alpha power transformed family, is explored in detail. It is of particular interest because there are a variety of possible symmetrical and asymmetrical forms for the density function of this distribution. The proposed distribution is loaded with several features. Maximum likelihood, least squares, weighted least squares, and Cramer-von Mises are the four techniques used to estimate the parameters of the new model. A simulation study has been conducted to assess its effectiveness. Actuarial measures like value at risk and tail value at risk are also derived. Compared to other recently introduced heavy-tailed distributions, the tail of the proposed distribution is heavier. Moreover, the model's usefulness is investigated using four real data sets from the fields of insurance, finance, and reliability. Compared to other well-known Lomax-based and competing distributions, the results demonstrate that the proposed distribution can fit the data better.