Functional classes of Lorenz curves are derived from a generalization of a relative poverty notion. All these Lorenz curves compare individual income to the average of all larger or all smaller incomes. The parameters of the Lorenz curves are effectively computed from empirical income data by least square regressions. Best fits are analyzed and resulting functional Gini indices are compared to empirical Gini indices.First version received: September 2002/Final version received: April 2003