Full text: The Personal Distribution of Income

2 
income in 
year t 
income in year t+1 
Q V 1 2 3 4 5 6 
0 
1 
2 
3 
4 
5 
q 
q 
q 
q 
q p 
q p 
p 
p 
p 
p 
A 
We now re-interpret this matrix so that the states of the 
system are not the incomes but the stages in a hierarchy 
or the seniority,a kind of'age",which,however,as we shall 
see later,is linked to the income.Let us assume only two 
alternative possibilities of transition for a person in 
this system:Either a rise from one stage in one year to 
the next higher stage in the next year which has 
probability p; or the death of the person,i.e. transition 
to the zero class which has probability q (p+q =1). 
In addition there are new entries from the zero class to 
replenish the stock of persons. The entries are supposed 
to compensate the exits of persons so that the stock 
remains constant. 
In this form the model is exactly the same as a renewal 
process described by Feller in the following terms (Feller 
1968 Vol I XV.3,p.382):The state E k represents the age of 
the system. When the system reaches age k it either
	        

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