The odd exponentiated Rayleigh-G family: A flexible statistical framework for reliability and radiation modeling

This study introduces a new and highly adaptive family of continuous probability distributions, known as the odd-exponent Rayleigh-G (OERG) family. Developed using the TX transform with exponential Rayleigh density as the generator, this family offers three additional formal parameters, significantly enhancing its modeling capabilities for any fundamental distribution. The study systematically relies on a comprehensive mathematical framework, including cumulative distribution function (CDF), probability distribution function (PDF), quantile functions, explicit moment expressions, the general moment function, Rényi entropy, and others. The distribution parameters were estimated using maximum likelihood (MLE), least squares (LSE), and weighted least squares (WLSE). After applying various estimation methodologies, the MLE clearly outperformed the others in terms of estimation accuracy, making it the optimal choice going forward. This superiority enables the OERG family of algorithms to be a powerful and flexible statistical tool for researchers. It empowers them to perform reliable statistical analysis of complex data in vital fields such as reliability analysis and radiation analysis.