DUS Kumaraswamy-G Family of Distributions: Baseline Extension, Statistical Properties, Estimation Techniques, Actuarial Risk Measures, and Applications to United Kingdom Economic Sector Data

In this paper, we have proposed a new family of probability distribution, known as the Dinesh–Umesh–Sanjay (DUS) Kumaraswamy-G (DUSK-G) family, which serves as a flexible extension of the DUS generator. As a special case, we introduce the DUS Kumaraswamy Weibull (DUSKW) distribution obtained by applying the proposed transformation to the Weibull distribution. The DUSKW model offers enhanced flexibility for analyzing diverse lifetime and reliability datasets. Various statistical properties of the new distribution are derived and discussed in detail with some actuarial measures studied. To estimate the model parameters, six different methods are considered. A Monte Carlo simulation study, implemented through the nlminb function in R with the L-BFGS-B optimization algorithm, is carried out to evaluate the performance of these methods under different parameter settings and sample sizes. The practical applicability of the DUSKW distribution is demonstrated using Wholesale, Food Chain, Kevlar, and BTC-USD datasets. Model adequacy and selection are assessed using various information criteria and goodness-of-fit statistics, and the results confirm that the proposed distribution consistently provides a superior fit compared with the classical Weibull and other competing models.