A Flexible Extension of the Log-Logistic Distribution with Application to Cancer Data

Akeem Ajibola  Adepoju; Mohamed A. F.  Elbarkawy; Aliyu Ismail  Ishaq; Narinderjit Singh  Sawaran Singh; Hanita  Daud; Ahmad Abubakar  Suleiman; Ehab M.  Almetwally; Mohammed  Elgarhy

doi:10.6000/1929-6029.2025.14.59

Authors

Akeem Ajibola Adepoju Department of Statistics, Aliko Dangote University of Science and Technology, Wudil, 713281, Nigeria
Mohamed A. F. Elbarkawy Department of Insurance and Risk Management, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Aliyu Ismail Ishaq Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
Narinderjit Singh Sawaran Singh Faculty of Data Science and Information Technology, INTI International University, Persiaran Perdana BBN Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia
Hanita Daud Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Malaysia
Ahmad Abubakar Suleiman Department of Statistics, Aliko Dangote University of Science and Technology, Wudil, 713281, Nigeria
Ehab M. Almetwally Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Mohammed Elgarhy Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt

DOI:

https://doi.org/10.6000/1929-6029.2025.14.59

Keywords:

Log-logistic distribution, Topp-Leone-G family, maximum likelihood, ordinary least square, infectious disease, public health

Abstract

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.

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