Bayesian and classical inference for some inequality measures

Abstract

The present study demonstrates some results using Bayesian and classical inference in the context of inequality measures. There are number of income inequality measures but Lorenz Curve and related Gini Index still remain the most popular measures among the researchers due to their straightforward behavior of interpretation and good statistical properties. Some other income inequality measures and variants of Lorenz Curve viz. Bonferroni Curve, Cumulated Mean Income Curve, and Zenga Curve and their corresponding indices having interesting characteristics have also caught the attention of researchers in recent times. In the present study the Bayesian approach for these well-known measures of income inequality for different distributions under different priors and loss functions is discussed and some new techniques are proposed using Bayesian and Classical inference. newlineIn first two chapters, Bayesian and Semi-Bayesian approach is used for estimation of the Gini index and the Bonferroni index for the Dagum distribution using informative and non-informative priors. HPD credible intervals are also obtained for both the inequality measures using simulation and real life data set. In another chapter different sampling schemes such as systematic sampling (SYS) and ranked set sampling (RSS) are being used for calculating the inequality indices. Monte Carlo simulation approach is used to obtain relative efficiency and comparison with that of simple random sample estimators. Bayesian estimators of the parameters as well as of some inequality measures such as Gini index and Bonferroni index using upper record values have been obtained for Fréchet, Power I and Pareto I distributions in another chapter. In the last chapter some new process capability indices are proposed using Gini Mean difference and their Bayesian estimation is carried out for exponential and uniform distributions. newline newline