Topp-Leone distribution proposal for the transmuted lower records type with practical application

Abstract

This study proposes and applies a new probability distribution, referred to as the Topp–Leone distribution with Transmuted Lower Record Type transformation (TLRT–Topp-Leone). The proposed model extends the flexibility of the classical Topp–Leone distribution by incorporating a mathematical transformation that enhances its ability to capture asymmetric and heavy-tailed data. The theoretical framework provides a comprehensive derivation of the main statistical properties, including the probability density function, cumulative distribution function, and survival function, in addition to the formulation of the maximum likelihood estimation (MLE) method for parameter estimation. On the empirical side, real survival data of 150 COVID-19 patients admitted to Al-Hussein Hospital in Karbala during the period 2020–2024 were analyzed. The performance of the proposed model was evaluated against the original Topp–Leone distribution using the Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests, as well as the information criteria AIC, BIC, and CAIC. The results demonstrated that the TLRT–Topp-Leone distribution provides a superior and more accurate fit to the observed data. Consequently, the proposed model constitutes a significant contribution to the family of flexible probability distributions and offers wide potential for applications in medical survival analysis and applied statistics