A modified Weibull distribution under competing risks

Abstract

In this paper, we introduced a modified Weibull distribution which is capable of handling both unimodal and bimodal scenarios. The hazard function for this distribution exhibits versatile behaviors, including increasing, decreasing, bathtub-shaped, and increasing-decreasing-increasing patterns. This modified distribution is applied in a competing risks framework with two causes of failure. Maximum Likelihood Estimation (MLE) is used for parameter estimation, and due to the lack of explicit solutions, we employed the Newton-Raphson algorithm. To validate the modified Weibull distribution, we conducted a simulation study and analysed a real-life dataset of cancer patients.