Bayesian analysis of Generalized Modified Weibull Distribution Under Censored Data and Presence of Covariates

The generalized modified Weibull (GMW) distribution extends the modified Weibull distribution by offering a hazard function with various shapes, including constant, increasing, decreasing, unimodal, and bathtub. This paper aims to estimate the four unknown parameters of the GMW distribution using a Bayesian approach, assuming a lack of prior information represented by noninformative priors such as Jeffreys, Uniform, and Gamma priors. The Bayesian analysis considers both censored data and the presence of covariates. The results of the Bayesian inference are compared with those of the maximum likelihood approach. The Markov Chain Monte Carlo (MCMC) algorithm is employed to compute the Bayesian estimators and construct credible intervals. A simulation study evaluates the performance of these estimators, with comparisons made based on bias, mean square error, and coverage probability. Real data sets are analyzed for illustrative purposes.