This paper proposes a new bounded probability model, the Unit-Weighted Lomax (UWLx) distribution, constructed via transformation of the weighted Lomax distribution. The UWLx distribution is designed for data restricted to the unit interval and provides greater flexibility in representing diverse behaviors of density and hazard functions, including monotonic and bathtub-shaped forms. Key statistical properties such as survival and hazard rate functions, moments, and order statistics are derived. Parameter estimation is addressed through the maximum likelihood method, and a simulation study confirms the consistency and efficiency of the estimators. The practical utility of the model is demonstrated through an application to COVID-19 recovery rate data, where the UWLx distribution is compared against well-known unit distributions, including the Beta, Kumaraswamy, and Unit Weibull. Model selection criteria and goodness-of-fit tests show that the UWLx distribution yields a superior fit, underscoring its potential as a versatile tool for analyzing bounded data in medical, reliability, and related fields.
Kilany et al. (Wed,) studied this question.