Statistical analysis of disability: Utilizing the modified kies power unit inverse Lindley model

In this article, we propose a new extension of a new unit probability statistical model, the so-called modified kies power unit inverse Lindley (MKPUILD) distribution. The MKPUILD is very flexible model because it’s probability density function and hazard rate function have different shapes as unimodal, right-skewed, left-skewed, bathtub, increasing, N-shaped. The new suggested model is very flexible and suitable for the disability data in the Kingdom of Saudi Arabia. This study demonstrates the flexibility and applicability of the MKPUILD by analyzing two real-world datasets: the relative distribution of individuals with mild difficulties and the relative distribution of individuals with disabilities in Saudi Arabia, categorized by age groups. These data sets exhibit diverse statistical characteristics, enabling a comprehensive evaluation of the performance of the model. To validate the efficacy of the proposed model, goodness-of-fit statistics were utilized, comparing the MKPUILD with existing competing models. The findings highlight the robustness of the MKPUILD in capturing complex statistical patterns across varying datasets. The model parameters are determined by several estimation techniques. Simulation tests were performed using MKPUILD to analyze the efficacy of various estimation techniques. The essential characteristics of the model have been established, including the quantile function, moments and order statistics.