Data augmentation based methods for estimating the parameters of the Feller-Pareto distribution: theory and applications

Abstract

AbstractIn income and wealth data modeling Pareto distribution and its several variants play an important role. Both univariate and multivariate variations of this model have been extensively used as a suitable model for various non-negative socio-economic variables. In this article, we consider the most general Feller-Pareto (FP, in short) distribution, which subsumes all four types of Pareto distributions and show that it can be represented as a mixture of a conditional generalized gamma and an unconditional gamma distribution. Using this strategy, we consider a data augmentation based method (under the envelope of Bayesian paradigm) to estimate the parameters of the FP distribution. This mixture representation allows us to easily derive conditional Jeffery’s type non informative priors. For illustrative purposes, one data set is considered to exhibit the utility of the proposed method.

Keywords

• Pareto distribution
• Feller-Pareto distribution
• data augmentation
• Bayesian estimation
• Convergence of MCMC procedure