A Flexible Extension of the Log-Logistic Distribution with Application to Cancer Data - Adepoju, Akeem Ajibola; Elbarkawy, Mohamed A. F.; Ishaq, Aliyu Ismail; Sawaran Singh, Narinderjit Singh; Daud, Hanita; Suleiman, Ahmad Abubakar; Almetwally, Ehab M.; Elgarhy, Mohammed (International Journal of Statistics in Medical Research, 2025)
This article introduces the Type II Half Logistic Topp-Leone-G (TIIHLTL-G) family, which unifies the structural properties of the Type II Half Logistic-(G TIIHL-G) and Topp-Leone-G (TL-G) family of distributions. The novelty of the TIIHLTL-G family lies in its enhanced shape flexibility and ability to model various skewness and kurtosis patterns beyond those captured by existing extensions. The statistical features of the new TIIHLTL-G family have been thoroughly investigated, including the probability-weighted moment, hazard function, moments, order statistics, quantile function, and survival function. Parameters are estimated using classical techniques, with maximum likelihood estimation performing best overall. Application to two real cancer datasets demonstrates the superiority of the proposed model over competing distributions, including the Log-logistic and related variants, with lower AIC, and BIC confirming its improved goodness-of-fit and predictive accuracy.