Semi-parametric estimation of the Quintile Share Ratio index of inequality measure for heavy-tailed income distributions with index in the upper half of the unit interval

Abstract

Kpanzou (2014) proposed an asymptotic \(alpha\) stable distribution for the nonparametric Quintile Share Ratio (QSR) estimator in the case of heavy-tailed distributions. It is well known that the heaviness of the distribution tails is controlled by an unknown parameter called tail index. To better understand the behavior of the distribution tail and the inequality of capital incomes, we introduce, in this paper, semi-parametric estimators of the QSR index which take into account the estimation of that tail index, and we study their asymptotic normality. A small simulation is conducted to illustrate the performance of our method.