Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T02:41:53.548Z Has data issue: false hasContentIssue false
  • English
  • Français

On a model for a fair distribution of gifts

Published online by Cambridge University Press:  14 July 2016

János Galambos
János Galambos*
Affiliation:
Temple University, Philadelphia
Get access Rights & Permissions [Opens in a new window]

Extract

A number of items are to be distributed among n individuals, arranged in a line and labelled by the integers 1, 2, ···, n, in such a way that the distance between any two members presented should be at least d, a given number, but otherwise any subset of the population should have the same probability of each of its members being presented. The number of items thus distributed is a random variable X(d, n) and it turns out that X(d, n) is asymptotically a fixed percentage of the population size n. This fact makes it possible to apply the model in a number of situations. For example, if in a foreign aid program a number of tools are offered and to be distributed in a fair way but, for lack of sufficient quantity, one tool is expected to be used by a number of neighbours, the model is applicable if the amount of aid is not fixed in advance but may vary within certain limits. A similar situation arises in cases of disaster (floods, earthquakes, etc.) when the victims are sent gifts, again in an insufficient quantity, hence for the sake of justice, a family of a smaller size is supposed to receive only one gift. In many other similar cases, the model can be used.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 681 - 690
Copyright
Copyright © Applied Probability Trust 1971 

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] Daykin, D. E. (1960) Representation of natural numbers as sums of generalized Fibonacci numbers. J. London Math. Soc. 35, 143–160.Google Scholar
[2] Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vol. I, 2nd ed., Wiley, New York.Google Scholar
[3] Galambos, J. (1970) The occurrence of a renewal process in the theory of numbers. Abstract. Ann. Math. Statist. 41, 1784.Google Scholar
[4] Galambos, J. (1971) A generalization of a theorem of Borel concerning the distribution of digits in dyadic expansions. Amer. Math. Monthly, 78 (To appear).Google Scholar