Inference on modified Weibull type distribution and its application to Competing risks data using MCMC

For lifetime data analysis, failure time analysis, or survival analysis, the Weibull distribution is commonly used due to its various hazard functions, which can be increasing, decreasing, or constant. We have extended the traditional twoparameter Weibull distribution to accommodate hazard functions that are increasing, decreasing, constant and bathtubshaped. Utilizing a competing risks approach, we applied this modified Weibull distribution to both simulated data and an observed mice dataset. Our findings indicate that the modified Weibull distribution provides a better fit to the mice dataset compared to the traditional Weibull distribution. We estimated the parameters of the modified Weibull distribution using Maximum likelihood estimation (MLE) and Bayesian methods. For MLE, we employed the Newton-Raphson numerical method, while for the Bayesian approach, we used the Metropolis-Hastings algorithm, an MCMC method. Additionally, we plotted hazard curves for both the simulated and mice datasets. The Kaplan-Meier survival curves were plotted along with the survival curve of the modified Weibull distribution.. KEYWORDS :Modified weibull distribution, Competing risks, MCMC, Information criterion, MLE.