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

Colm Art O’Cinneide | Zendy; Helmut Schneider | Zendy

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

Author(s) -

Colm Art O’Cinneide,

Helmut Schneider

Publication year - 1987

Publication title -

operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.797

H-Index - 140

eISSN - 1526-5463

pISSN - 0030-364X

DOI - 10.1287/opre.35.3.445

Subject(s) - poisson distribution , binomial (polynomial) , convolution (computer science) , negative binomial distribution , computer science , algorithm , mathematics , poisson binomial distribution , statistics , beta binomial distribution , artificial intelligence , artificial neural network

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.

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