On fitting disability in Saudi Arabia and radiation data: Using the alpha power transformed Rayleigh inverted Weibull distribution

This study presents an in-depth analysis of the distribution of disability in Saudi Arabia according to age groups, as documented in the latest KSA Census of 2022. “4.2%” of the population of the Kingdom experiences difficulties or disabilities. The prevalence of disabilities increases significantly with age, where the percentage of people with disabilities is very low in the younger age groups and increases dramatically among the older individuals. These findings provide valuable information for policy makers in developing targeted intervention programs for people with disabilities based on age groups. Traditional probability distributions may, on occasion, fail to take into account this complexity, which can lead to inaccurate conclusions being drawn instead. So, in this article, we introduce a new three-parameter model called the alpha-power transformed Rayleigh inverted Weibull distribution (APTRIWD) to solve this issue. The probability density curves of APTRIWD provide evidence that it can be used in the analysis of disability data in Saudi Arabia and radiation data, demonstrating its practical applicability. Due to the fact that the hazard rate function (HRF) for APTRIWD can exhibit J-shaped, growing, and declining patterns, researchers have a great deal of flexibility when it comes to constructing statistical models for research on disability concerns. Some important statistical properties of the new suggested model are discussed. The maximum likelihood estimation method is utilized to determine the parameters of the machine learning model. For the purpose of determining the efficiency of maximum likelihood estimators, a Monte Carlo simulation analysis is performed. The proposed distribution was evaluated using three datasets related to disability concerns in Saudi Arabia and radiation data. The APTRIWD exhibited superior goodness of fit compared to several models. The APTRIWD is recommended for data modeling in fields such as disability challenges due to its exceptional fit capabilities and radiation data.