The Personal Distribution of Income

Steindl, Josef

Bibliographic data

Works

Document type:: Works

Collection:: Josef Steindl Collection

Title:: The Personal Distribution of Income

Author:: Steindl, Josef

Scope:: Typoskript, 24 Seiten (23 Seiten auf Durchschlagpapier), mit zahlreichen handschriftlichen Anmerkungen und Anstreichungen

Year of publication:: 1972

Source material date:: August-September 1972

Language:: English

Note:: Unveröffentlichtes Typoskript.

Topic:: Stochastic processes and size distribution

Shelfmark:: S/M.52.8

Use and reproduction license:: In Copyright

Access:: Free access

DOI:: https://doi.org/10.48671/nls.js.AC14446372

There are only two alternative transition for a person in this system: Either a rise of income from one year to the next (note that the income classes are on the log scale) which has probability p; or death of the person, i.e. transition to the zero class, which has probability q (p + q = 1). In addition, there are entries from the zero to class^replenish the stock of income receiveif. The essence of this- model is described by Feller 1 ^ in the following terms: The state represents the age of the system. When the system reaches age K, it either continues to age or it rejuvenates and starts afresh from age zero. The successive passages through the zero state represent a recurrent event. The probability that the recurrence time equals a, is i 'q. We are interested in the question: How many years have passed, i.e. how many income steps have been mounted, since the last rejuvenation? This is the "spent waiting time” of the renex^al process. Choosing an arbitrary starting point we can say that in the year n the system will be in state E/t if and only if the last rejuvenation occured in year n-M,. Letting n-K increase we obtain in the limit the steady state probability of the'fepent waiting time" £ ^. It is proportionate !) Z"7 7 Vol. I. 2?.3, p. 382. 2 V^T7 Chapter V.

Access restriction

Copyright

fullscreen: The Personal Distribution of Income

Works

Downloads

Full record

This page

Image fragment

Formats and links

Formats

Links

Cite

Full record

This page

Citation recommendation