Introducing the unit Zeghdoudi distribution as a novel statistical model for analyzing proportional data

Abstract

Unit distributions are essential in statistical modeling, providing a robust framework for understanding variables constrained within the unit interval [0,1]. This interval is crucial in public health, environmental studies, engineering, and finance, where measurements often represent proportions, probabilities, or rates. Despite numerous unit distributions derived by transforming existing distributions, there remains a pressing need for new distributions that can accommodate the unique characteristics of diverse datasets. In this study, we introduce the unit Zeghdoudi distribution (UZD), a novel transformation of the Zeghdoudi distribution (ZD). This new distribution retains the simplicity of the original ZD while offering enhanced flexibility and precision in modeling data confined to the unit interval. The UZD exhibits several noteworthy features, including both right and left-skewed probability density functions, a closed-form quantile function, easily defined moments, and manageable entropies. Using sixteen classical methods for parameter estimation, supported by a comprehensive simulation study, we demonstrate the efficiency and reliability of the UZD. Finally, the application of the UZD to three real-world proportional datasets related to (COVID-19, environmental, and radiation datasets) underscores its effectiveness and demonstrates its superiority over several established models.