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RANDOM FINITE SUBSETS WITH EXPONENTIAL DISTRIBUTIONS

Published online by Cambridge University Press:  15 December 2006

Kyle Siegrist
Kyle Siegrist
Affiliation:
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL, E-mail: siegrist@math.uah.edu
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Abstract

Let S denote the collection of all finite subsets of . We define an operation on S that makes S into a positive semigroup with set inclusion as the associated partial order. Positive semigroups are the natural home for probability distributions with exponential properties, such as the memoryless and constant rate properties. We show that there are no exponential distributions on S, but that S can be partitioned into subsemigroups, each of which supports a one-parameter family of exponential distributions. We then find the distribution on S that is closest to exponential, in a certain sense. This work might have applications to the problem of selecting a finite sample from a countably infinite population in the most random way.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 1 , January 2007 , pp. 117 - 132
Copyright
© 2007 Cambridge University Press

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References

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