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

Rights of use:: In Copyright

Access:: Free access

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

4 the low income of new entrants. In fact the role of new entry is crucial not only in this model but in other applications as well ( size of firms, towns, wealth ). H.Simon (1955) studied the number of times a particular word (vocable) occurs in a text. The number of vocables which occur with a given frequency decreases with that frequency in a Pareto like fashion. Simon’s treatment is based on the work of Yule ( 1924 ) who dealt with a biological problem : The frequency of genera with different number of species which is distributed according to Pareto. He explained this pattern by means of a pure birth process deriving from this the Yule distribution with density f(n) = 0( f""'(1 + o4 ) n -1- ° i ' as n “. The model of evolution assumes that mutations occur randomly with a frequency g per time unit, creating new genera, and with a frequency s per time unit creating new species, where g ^ s . Since each species has the same chance of creating a new species we have here a proportionate growth, in analogy to the law of proportionate effect. The steady state is produced by the emergence of new geqera. The Pareto coefficient equals the ratio of the frequencies with which the two kind?of mutations appear, that is g/s. Simon whose merit it is to have drawn attention to this brilliant work has suggested application to incomes ( not very convincingly ) and has himself applied it to firm sizes (1967). A very direct application relates to the size of “the "number of Ct ( / lt> ~u ( £f L S 'J *

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