By Barry C. Arnold
A variety of papers on Pareto distributions and similar themes have seemed because the first version of this hadbook. This ebook updates the preferred first version through interleafing advancements inequality indices, parametric households of Lorenz curves, Pareto techniques, hidden truncation, and more.
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Extra resources for Pareto Distributions Second Edition
Hagstroem (1960) mentioned both possibilities. Ericson had mixed success in his efforts to fit observed income distributions by his exponential model. Hagstroem (1960) flatly stated that the fit is unsatisfactory and discarded the model in favor of a Pareto model. The model can survive in a modified sense. Observed distributions might well be mixtures of distributions, which do arise by a coin shower mechanism. The resulting mixed exponential can have Pareto-like tail behavior. As mentioned in Chapter 1, use of a gamma mixing distribution leads to a Lomax or Pareto (II) distribution.
Pareto’s suggested laws will not be included in our list of models. In the final section of this chapter we will list several families of distributions which have been proposed as candidates for fitting or graduating income distributions, usually with little indication as to why the fit should be good. The two Pareto laws will appear in this list. The title, “model,” in this chapter, will be reserved for stochastic mechanisms which mirror, to some extent, socio-economic forces which affect income and which lead to delineation of at least some properties of resulting income distributions.
A general trend of diminution of income inequality can be observed in the twentieth century (see Hagstroem, 1960). Watkins proposed instead that one plot log u against log L(u). These plots in his experience were approximately linear, and the corresponding slope could be used as a summary measure of concentration. Gini (1909) proposed a new summary index of inequality or concentration. It was not however the one which is now associated with his name. Perhaps tacitly assuming an underlying Pareto distribution, his index was obtained by plotting F(x), the proportion of people whose incomes exceed x, against F 1 (x), the proportion of the income of the population obtained by those individuals whose incomes exceed x.
Pareto Distributions Second Edition by Barry C. Arnold