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On the variance of a trimmed Poisson distribution

Published online by Cambridge University Press:  14 July 2016

J. H. B. Kemperman
J. H. B. Kemperman*
Affiliation:
University of Texas, Austin
*
∗Permanent address: University of Rochester, Rochester, N.Y. 14627, U.S.A.
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Abstract

Consider a queue for a special performance or sale. A person with arrival number i will decide to join the queue with probability pi. Here the pi denote fixed constants. Let X denote the number of arrivals, X″ the number of customers leaving the queue and X′ = X – X″ the number of customers who stay with the queue. For the case that pi+1 ≦ pi and X has a Poisson distribution, it is shown that Var (Xʺ) ≧ E(Xʺ) and Var (X′) ≦ E(X′). There are also results for the case where {pi} and X are rather arbitrary.

Keywords

QUEUE WITH BALKINGTRUNCATED POISSON DISTRIBUTIONMONOTONE TRIMMING OF A POISSON DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 220 - 225
Copyright
Copyright © Applied Probability Trust 1979 

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References

Hardy, G. H., Littlewood, J. E. and Pólýa, G. (1934) Inequalities. Cambridge University Press.Google Scholar