Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T22:16:34.210Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

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

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