Pareto Distribution

Steindl, Josef

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Document type:: Works

Collection:: Josef Steindl Collection

Title:: Pareto Distribution

Author:: Steindl, Josef

Scope:: Typoskript, 9 Seiten (mit einer handschriftlichen Korrektur auf Seite 4) sowie eine Seite mit handschriftlichen Notizen

Year of publication:: 1987

Shelfmark:: S/M.52.12

DOI:: https://doi.org/10.48671/nls.js.AC14446378

Pareto Distribution Using certain data on personal income V.Pareto (1897 ) plotted income on the abscissa and the number of people who received more than that on the ordinate of logarithmic paper and found a roughly linear relation. This Pareto distribution or Pareto law may be written as —* / . . x = a y or log x = a — log y (1) where oi ( the negative slope of the straight line ) is called the Pareto coefficient. The density of the distribution is dx = a c< y dy irv The Pareto coefficient is occasionally used as a measure of inequality: The larger 0( the less unequal is the distribution. According to Champernowne 0( is useful as a measure of inequality for the high income range whereas for medium and low incomes other measures are preferable (Champernowne 1952 ). (£ takes only positive values. If o( ^ 2 the distribution has no variance; if oC ^ 1 it has no mean either. In practice the Pareto law applies only to the tail of the empirical distributions i.e. to incomes above a certain size. Thus the law (1) is valid assymptotically as y —^ oo The range in which the empirical distributions conform i to thejlaw is different in different cases. It seems to be larger for wealth than for income ( perhaps because we have only data for large wealth ) and even larger for tuwns. In the case of firm sizes only the very large firms are covered by the law.

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