Hierarchical Bayesian models for small area estimation with GB2 distribution

We present predictive hierarchical Bayesian models to fit continuous, and positively skewed size data from small areas with the generalized beta of the second kind (GB2) distribution. We discuss three different GB2 mixture models. In the models, we have implemented the technique of small areas estimation. The posterior distributions of these models are complex. We have used Taylor series approximations, grid sampling and Metropolis samplers to fit the models. We have applied our models to the per-capita consumption size data from the second Nepal Living Standards Survey. We choose the best fitted model from the three GB2 mixture models. With the best fitted model, we provide small area estimation of poverty indicators by linking the survey data with the census data. A simulation study is provided.