The Gini Index for a Quadratic Pen's Parade

In this paper, we provide alternative derivations of the Gini index for a quadratic Pen's parade without imposing unnecessary restrictions on its parameters. It turns out that in sufficiently large samples the reference value of the Gini index for a quadratic Pen's parade is 1/2 (as opposed to 1/3 in the case of a linear Pen's parade). Whether the Gini index is equal to, less than or greater than the reference value in these cases depends on whether or not Pen's parade passes through, above or below the origin, respectively.