Bayesian Nonparametric Model for Weighted Data Using Mixture of Burr XII Distributions

Dirichlet process mixture model (DPMM) is a popular Bayesian nonparametric model. In this paper, we apply this model to weighted data and then estimate the un-weighted distribution from the corresponding weighted distribution using the metropolis-Hastings algorithm. We then apply the DPMM with different kernels to simulated and real data sets. In particular, we work with lifetime data in the presence of censored data and then calculate estimated density and survival values.