The Modified Log-Logistic Distribution: Properties and Inference with Real-Life Data Applications

Abstract

This paper introduces a new three-parameter extension of the log-logistic distribution called the generalized Kavya-Manoharan log-logistic distribution. The proposed distribution extends the Kavya-Manoharan log-logistic model, and its density exhibits symmetric, right-skewed, reversed-J, and left-skewed shapes. Its hazard function can provide non-monotonic and monotonic shapes, which makes it particularly valuable for accurately modeling complex time-to-event data. Several distributional properties are addressed. The introduced model parameters are estimated via eight frequentist estimation approaches. Moreover, extensive simulations are obtained to explore the performance of the proposed methods of estimations. Finally, the performance of the proposed distribution is investigated using three real-lifetime datasets from medicine and reliability engineering. The analyzed data illustrated that the proposed distribution provided an adequate fit as compared to other competing log-logistic distributions.