Kumaraswamy Heavy-Tailed-G Family of Distributions: Theory, Estimation, and Real-World Applications

Source abstract

This paper introduces a new family of distributions, the Kumaraswamy heavy-tailed-G (KHT-G) family, constructed by combining the Kumaraswamy-G and heavy-tailed-G generators. Its density function is expressed as an infinite linear combination of exponentiated-G densities, a formulation that facilitates the derivation of key statistical properties. We derive the statistical properties of the family, including the quantile function, moments, entropy, order statistics, and stochastic orderings, and demonstrate that its density and hazard rate shapes are highly flexible. Model parameters were estimated using five different methods, with an extensive Monte Carlo simulation study establishing maximum likelihood estimation as the most effective. We also derive essential actuarial risk measures, and numerical simulations confirm that the KHT-G family possesses heavier tails than competing models, making it particularly suitable for modeling extreme events. The practical utility of the Kumaraswamy heavy-tailed-Weibull (KHT-W) sub-model is demonstrated through applications to two real-world datasets, where it significantly outperformed established models. The KHT-G distribution shows substantial potential for applications in finance, insurance, and health sciences.