Mixtures density estimation in lifetime data analysis: an application of nonparametric Bayesian estimation technique

In this paper we review a nonparametric Bayesian estimation technique in mixture of distributions employing a flexible Dirichlet process mixture. Methods for simulation based model fitting, in the presence of censoring, and for prior specification are provided. Using the method it allows dealing with a variety of practical issues including estimating density function, survival function, hazard function etc. Our interest on the other hand is to identify the underlying components of mixtures in a dataset by mixture model analysis. We thus illustrate our model with a simulated and a real data set under Type I censoring considering mixture of Weibull distributions. These illustrations demonstrate that modeling data in an infinite mixture works well when there are only a small finite number of components in the true mixtures.