Full text: Pareto Distribution

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 
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