Bayesian Inference of the Weibull-Pareto Distribution

Bayesian Inference of the Weibull-Pareto Distribution Weibull distribution has been extensively used over the past decades for modeling lifetime data. It has intensive application in the field of biological studies, reliability engineering, general insurance, electrical engineering, and industrial engineering. Recently, a new distribution, namely, Weibull-Pareto distribution has been introduced in the literature. Depending on the value of its parameters, this distribution can be implemented to model highly skewed (left or right) data. This type of skewed distribution is typical when dealing with survival and actuarial data. In this paper we introduce a hierarchical Bayesian model for estimating parameters of the Weibull-Pareto distribution. We introduce appropriate prior distributions for the model parameters. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. This model is illustrated by survival data from patients diagnosed with cutaneous melanoma. We further compare the performance of the proposed model with other competing models in simulated data sets. Keywords: Weibull-Pareto, hierarchical Bayesian model, right censored, survival data, MCMC