A family of arctan Lorenz curves

Abstract

This paper presents a new family of parametric Lorenz curves based on the arctan function and adding a parameter - ∞< α< ∞, α≠ 0 to an initial Lorenz curve L0(p),0≤p≤1. The particular case obtained when α tends to zero is reduced to the initial Lorenz curve L0(p). The corresponding distribution functions are shown. Some inequality measures are calculated, and a method to compute the Gini index based on the use of the inverse of the Lorenz curve is proposed. Finally, an application to two well-known data sets is presented and a good fit is obtained.