The Generalized Unit Weibull Distribution: Properties, Estimation, and Applications in Actuarial Science and Insurance

Abstract

This study introduces the Generalized Unit Weibull (GUW) distribution, an extension of the Unit Weibull distribution achieved through transformation and the inclusion of additional parameters. We explore key theoretical properties of this novel distribution, including stochastic functions, quantile functions and measures, moments, and Rényi entropy. The model's unknown parameters are estimated using the maximum likelihood method. To demonstrate its applicability, we compare the proposed model with existing alternatives using two real-world data sets, particularly in actuarial science and insurance.