ABSTRACT

In this chapter we will introduce a hierarchy of successively more complicated Pareto distributions. We begin with the classical Pareto distribution and, by the introduction of parameters which relate to location, scale, Gini index and shape, progress to a family called the Pareto IV family (essentially the Burr distributions). It turns out, that for purposes of deriving distributional results, it is sometimes convenient to consider an even more general family, which is here called the Feller-Pareto family. The full five-parameter Feller-Pareto distribution has, to the author’s knowledge, not much been used for fitting income data. (It should do well, when it is used, since with 5 parameters you could fit just about any unimodal distribution!) This chapter draws heavily on the material in Arnold and Laguna (1977).