Statistical analysis of disability: Utilizing the new extended Rayleigh inverted Weibull model - Mohamed A. Abdelkawy; Safar M. Alghamdi; Ibrahim Elbatal; Atef F. Hashem; Ahmed W. Shawki; Mohammed Elgarhy (Alexandria Engineering Journal, 2025)
In this article, we provide a novel distribution known as the new extended Rayleigh inverted Weibull (NERIW) distribution, which arises from the new extended family of distributions (NE-G). The shapes of the probability density function (PDF) can be decreasing, unimodal, or right-skewed, but the shapes of the hazard rate function (HRF) can be decreasing or upside down. The new model is investigated to identify its various statistical properties, including quantile function, median, moments, moment-generating function, incomplete, and conditional moments, mean deviation, and inequality measures. The model parameters are determined using the maximum likelihood estimation approach. A Monte Carlo simulation analysis is conducted to evaluate the effectiveness of maximum likelihood estimators. This study explores the effectiveness of the NERIW distribution in modeling health and disability statistics, focusing on two real-world datasets from Saudi Arabia. By comparing the NERIW distribution with alternative models and offering a more accurate representation of disability prevalence between age groups. The findings provide valuable information for policy makers and researchers in understanding disability trends and improving data-driven decision making in health planning.