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1 results

  • On the variance of a trimmed Poisson distribution

  • J. H. B. Kemperman
  • Journal:
    Journal of Applied Probability / Volume 16 / Issue 1 / March 1979
    Published online by Cambridge University Press:
    14 July 2016, pp. 220-225
    Print publication:
    March 1979

  • 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.