Statistical and reliability analysis of communication disability severity in Saudi Arabia using novel probability distribution

Understanding the distribution of communication disabilities is crucial for effective policy planning and resource allocation. This study introduces the Extended Generalized Inverted Kumaraswamy Standard Exponential (EGIKwS-Exp) distribution for modeling the percentage of Saudi individuals with severe or total communication disabilities aged two years and above across 13 administrative regions. The dataset, sourced from Disability Statistics 2023, exhibits significant variability, requiring a flexible probabilistic framework. The EGIKwS-Exp distribution, an extension of the exponential model, enhances adaptability for complex datasets like disability statistics. Key distributional and reliability properties, including hazard rate, reversed hazard rate, c umulative hazard, and survival functions, are derived. Parameter estimation is conducted using Maximum Likelihood Estimation, with Bayesian inference via MCMC Metropolis-Hastings, Asymptotic, Boot-P, Boot-T, and Highest Posterior Density confidence intervals ensuring robust analysis. Graphical reliability measures confirm the model's efficiency in capturing trends in communication disability data, offering a comprehensive framework for analyzing regional disparities and informing policymakers. By providing a robust statistical tool, this research supports more informed decision-making in disability studies and public health planning.