Full text: Pareto Distribution

3 
Thus it could be expected that the income of the various 
counties in England would be Pareto distributed because 
it results in each case from the addition of individual 
incomes which are Pareto distributed. 
Champernowne's pioneering work (1953) in essence goes back 
to his fellowship dissertation of 1936, published 1973. 
He builds on a tradition which explains the normal distribution 
as the result of the addition of random unit steps 
(left or right ) on the line over a long time ( random walk; 
for the terms and concepts relating to random processes 
refer to Feller Vol I ).If the random walk takes place on 
the logarithmic scale the distribution of the sum of steps 
will tend to log normality. This does not give, however, 
a stable distribution, because the dispersion will go on 
increasing all the time. Champernowne chooses the technique 
of the Markov chain: Each yearjs income depends only on the 
previous year's income/plus a random increment proportionate 
/ 
to last year's income; the probability of various increments 
remains constant from one year to the other. This feature 
is called the law of proportionate effect. Thus the required 
data will be embodied in a matrix which contains the 
probabilities of transition from one income in one year to 
another income in the following year. The number of 
income receivers remains stable in Champernowne's model 
because‘each exit is assumed to be automatically compensated 
by a new entry. To guaratee that the system reaches a 
steady state it is assumed that on the average the change of 
income is downwards; this is necessary to compensate the 
tendency of the system to diffusion which is characteristic 
of the unrestrained random walk. The assumption reflects
	        

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