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Technical Note—An Algorithm for Computing the Convolution of Poisson Negative Binomial and Geometric Distributions

Author

Listed:
  • Colm Art O'Cinneide

    (University of Arkansas, Fayetteville, Arkansas)

  • Helmut Schneider

    (Louisiana State University, Baton Rouge, Louisiana)

Abstract

We present a simple algorithm that computes the convolution of Poisson, negative binomial, and geometric distributions. We show that a certain infinite-server queue in a random facility repair environment has a steady-state distribution that involves such convolutions. The algorithm arises from the steady-state equations of this process.

Suggested Citation

  • Colm Art O'Cinneide & Helmut Schneider, 1987. "Technical Note—An Algorithm for Computing the Convolution of Poisson Negative Binomial and Geometric Distributions," Operations Research, INFORMS, vol. 35(3), pages 445-449, June.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:3:p:445-449
    DOI: 10.1287/opre.35.3.445
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