Bayesian inference for the finite gamma mixture model of income distribution

The income distribution model has provided an important aspect of economic inequality analysis. The determination of income inequality can be assisted by modeling a probability distribution of income which can be modeled by both parametric and nonparametric method. In the parametric perspective, the finite mixture distributions can perform a data-driven capability to model this income pattern of distributions which have particularly long-tailed, right-skewed and multimodal characteristics. The gamma distribution which has been widely used for estimating income distribution is used to develop the finite gamma mixture model which means the gamma distribution in each mixture component of the model. Bayesian approach pairs up with the Markov Chain Monte Carlo (MCMC) which has a valid inference without depending on normality asymptotic condition is used to estimate this finite mixture model. In this paper, the household income which was constructed based on the Indonesian Family Life Survey (IFLS) 2014-2015 data was utilized to show the work of the Bayesian inference performance through MCMC algorithm in estimating the parameter of the finite gamma mixture model. The goodness-of-fit comparisons of proposed finite gamma mixture models were made based on the widely applicable information criteria (WAIC).