The Frechet distribution with location parameter \(a\), scale parameter \(b\), shape parameter \(s\) and denoted as \(Frechet(a,b,s)\), where \(a>0\), \(b>0\) and \(s>0\), has a
probability density function given by (Kleiber and Kotz, 2003; Johnson et al., 1995)
$$f(y) = \displaystyle \frac{sb}{(y-a)^{2}} \left(\frac{b}{y-a}\right)^{s-1} \exp\left[- \displaystyle \left(\frac{b}{y-a}\right)^{s} \right],$$
and a cumulative distribution function given by
$$F(y)= \displaystyle \exp\left[- \displaystyle \left(\frac{b}{y-a}\right)^{s} \right],$$
where \(y > a\).
The Gini index, for \(s \geq 1\), can be computed as
$$G = 2^{1/s} -1.$$