  Widely used income inequality measure, Gini index is extended to form a
family of income inequality measures known as Single-Series Gini (S-Gini)
indices. In this study, we develop empirical likelihood (EL) and jackknife
empirical likelihood (JEL) based inference for S-Gini indices. We prove that
the limiting distribution of both EL and JEL ratio statistics are Chi-square
distribution with one degree of freedom. Using the asymptotic distribution we
construct EL and JEL based confidence intervals for realtive S-Gini indices. We
also give bootstrap-t and bootstrap calibrated empirical likelihood confidence
intervals for S-Gini indices. A numerical study is carried out to compare the
performances of the proposed confidence interval with the bootstrap methods. A
test for S-Gini indices based on jackknife empirical likelihood ratio is also
proposed. Finally we illustrate the proposed method using an income data.
