Novel Unit Distribution for Enhanced Modeling Capabilities: Healthcare and Geological Applications - Amal S. Hassan; Gaber Sallam Salem Abdalla; Abdoulie Faal; Omar A. Saudi (Engineering Reports, 2025)
ABSTRACT In statistical modeling, unit distributions are essential for evaluating proportional or rate‐based data in domains including public health, environmental science, and finance. While there are many different unit distributions, a scalable model is required to capture unique features in various data environments. This article introduces the unit inverse exponentiated Pareto (UIEP) distribution, a novel two‐parameter model. Unimodal, inverted J‐shaped, left‐skewed, and right‐skewed probability density functions, as well as rising, J‐shaped, or U‐shaped hazard rate functions, are some of the different shapes of the UIEP. Because of these adaptable features, it is more suited for unit data modeling. Stochastic ordering, quantiles, moments, probability‐weighted moments, significant uncertainty measures, Lorenz and Bonferroni curves, and stress‐strength reliability are among the key statistical features that are analytically generated. Statistical inference employed a number of methods, such as maximum likelihood, weighted least squares, Anderson‐Darling, least squares, and Kolmogorov, to estimate distribution parameters and assess different entropy measures. These statistical techniques make up an effective tool for academics and data analysts. Among these, simulation results indicated that the Kolmogorov method was the most effective for parameter estimation, particularly when combined with Arimoto, Rényi, Havrda‐Charvát, and Tsallis entropy measures. Furthermore, for low and high entropy orders, respectively, Arimoto and Rényi entropies performed better when maximum likelihood estimation was used. This result demonstrates a strong correlation between the most efficient estimator and the entropy order. Our results show that both the absolute bias and the mean squared error consistently decrease as the sample size increases. This pattern confirms that the provided estimation methods are reliable and consistent. To validate the proposed distribution, we applied it to two real‐world datasets: health data related to COVID‐19 and geological data from petroleum rock samples. These applications demonstrated improved model fit compared to alternative distributions.