Advancing reliability and medical data analysis through novel statistical distribution exploration

Abstract This comprehensive study delves into the examination and application of novel statistical distributions, namely the Ristić-Balakrishnan-Topp-Leone-Exponentiated half Logistic-G (RB-TL-EHL-G) family of distributions, emphasizing their paramount importance in reliability and medical data modeling. We meticulously explore a multitude of this family of novel distributions, accentuating their respective features, properties, and real-world applicability. The probability density, the cumulative distribution, the hazard rate, and the quantile functions are provided. The density functions of the RB-TL-EHL-G family are expanded, enabling a deeper understanding of their statistical properties, including various moments, generating functions, order statistics, stochastic orderings, probability weighted moments, and the Rényi entropy. A significant portion of the investigation is dedicated to the intensive analysis of various data sets, to which these distributions are fitted, unveiling noteworthy insights into their behavior and performance. Furthermore, the discussions extend to a comparative study, delineating the advantages and limitations of each distribution, fostering a deeper understanding and selection criteria for practitioners.