Bayesian analysis of mixtures of lognormal distribution with an unknown number of components from grouped data

TL;DR

This paper introduces a reversible jump MCMC method for estimating parameters of lognormal mixture models with unknown components, demonstrating accurate estimation and application to Japanese income data.

Contribution

It presents a novel Bayesian approach using reversible jump MCMC for mixtures with unknown components, specifically applied to income data analysis.

Findings

Parameters estimated accurately in simulated data

Posterior distributions closely match true distributions

Identified two income subgroups in Japanese data

Abstract

This study proposes a reversible jump Markov chain Monte Carlo method for estimating parameters of lognormal distribution mixtures for income. Using simulated data examples, we examined the proposed algorithm's performance and the accuracy of posterior distributions of the Gini coefficients. Results suggest that the parameters were estimated accurately. Therefore, the posterior distributions are close to the true distributions even when the different data generating process is accounted for. Moreover, promising results for Gini coefficients encouraged us to apply our method to real data from Japan. The empirical examples indicate two subgroups in Japan (2020) and the Gini coefficients' integrity.