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The Graduation of Income Distributions

Peter R. Fisk

Abstract

A variety of functional forms have been suggested, in the past, as suitable for describing distributions of income. Some have been derived from models "explaining" the generation of an income distribution, while others are claimed only to fit observations reasonably well. One which has not been widely considered is the sech square distribution. This distribution has certain useful characteristics, such as simple Lorenz measures of inequality and a simple method of graphical analysis, which make it a useful tool in examining and comparing distributions of income. The differential equation from which the sech square distribution is derived can be varied to allow a wide range of different distribution forms to be fitted. A similarity exists between this distribution function and the Pareto and Champernowne distribution functions. Some of the characteristics of the latter distribution are discussed in the paper.