Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T06:01:45.807Z Has data issue: false hasContentIssue false

Remarks on a model of competitive bidding for employment

Published online by Cambridge University Press:  14 July 2016

Anthony G. Pakes*
Affiliation:
The University of Western Australia
*
Postal address: Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia.

Abstract

Arnold and Laguna introduced a model for income distributions in which the income of the present generation of individuals has the same distribution as the minimum of a random number Nn of independent copies of some random variable and {Nn} is independent. The present paper gives a fairly complete analysis of this model and a number of extensions of it.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Arnold, B. C. (1982) Pareto Distributions.Google Scholar
[2] Arnold, B. C. and Laguna, L. (1976) A stochastic mechanism leading to asymptotically Paretian distributions. Business and Economics Sect., Proc. Amer. Statist. Assoc., 208210.Google Scholar
[3] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[4] Cohn, H. (1982) On a property related to a convergence in probability and some applications to branching processes. Stoch. Proc. Appl. 12 Google Scholar
[5] Dubuc, S. (1971a) La densité de la loi-limite d'un processus en cascade expansif. Z. Wahrscheinlichkeitsth. 19, 281290.CrossRefGoogle Scholar
[6] Dubuc, S. (1976) Problèmes relatifs a l'itération de fonctions suggérés par les processus en cascade. Ann. Inst. Fourier 21, 171251.CrossRefGoogle Scholar
[7] Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
[8] Goettge, R. T. (1975) Limit theorems for the supercritical Galton–Watson process in varying environments. Math. Biosci. 28, 171190.Google Scholar
[9] Johnson, N. L. and Kotz, S. (1970) Continuous Univariate Distributions—I. Houghton-Mifflin, Boston.Google Scholar
[10] Seneta, E. (1974) Regularly varying functions in the theory of simple branching processes. Adv. Appl. Prob. 6, 408420.Google Scholar
[11] Seneta, E. (1976) Regularly Varying Functions. Lecture Notes in Mathematics 508, Springer-Verlag, Berlin.CrossRefGoogle Scholar