  Given that the existing parametric functional forms for the Lorenz curve do
not fit all possible size distributions, a universal parametric functional form
is introduced. By using the empirical data from different scientific
disciplines and also the hypothetical data, this study shows that, the proposed
model fits not only the data whose actual Lorenz plots have a typical convex
segment but also the data whose actual Lorenz plots have both horizontal and
convex segments practically well. It also perfectly fits the data whose
observation is larger in size while the rest of observations are smaller and
equal in size as characterized by 2 positive-slope linear segments. In
addition, the proposed model has a closed-form expression for the Gini index,
making it computationally convenient to calculate. Considering that the Lorenz
curve and the Gini index are widely used in various disciplines of sciences,
the proposed model and the closed-form expression for the Gini index could be
used as alternative tools to analyze size distributions of non-negative
quantities and examine their inequalities or unevennesses.
