Actuarial and various entropy measures for a new extended log Kumaraswamy model: Properties and applications

This article introduces a novel extension of the log Kumaraswamy distribution, termed Marshall Olkin log Kumaraswamy $\left(MOL{k}_w\right)$. The mathematical and statistical characteristics of the suggested distribution are constructed, encompassing explicit formulations for quantiles, moments, conditional moments, as well as the Bonferroni and Lorenz curves. Five estimation methods for the model parameters have been derived. Entropy measures uncertainty and disorder in systems, playing a crucial role in fields such as statistics, economics, physics, and computer science. Rényi entropy is widely used in applications like statistical inference and pattern recognition. Accordingly, five entropy measures have been obtained for the $MOL{k}_w$ distribution A Monte Carlo simulation study is conducted to assess the efficacy of these estimators. Additionally, certain actuarial metrics, including value at risk and tail value at risk, are computed. Ultimately, applications of the model to actual data sets are provided to demonstrate the applicability and utility of the $MOL{k}_w$ distribution.