Poisson Random Variable

See: Random Variable, Poisson Probability Function, Poisson Experiment.

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References

2012

• http://en.wikipedia.org/wiki/Poisson_distribution#Generating_Poisson-distributed_random_variables
  • A simple algorithm to generate random Poisson-distributed numbers (pseudo-random number sampling) has been given by Knuth (Knuth, 1969):

    While simple, the complexity is linear in λ. There are many other algorithms to overcome this. Some are given in Ahrens & Dieter, see References below. Also, for large values of λ, there may be numerical stability issues because of the term e^−λ. One solution for large values of λ is Rejection sampling, another is to use a Gaussian approximation to the Poisson.

     Inverse transform sampling is simple and efficient for small values of λ, and requires only one uniform random number u per sample. Cumulative probabilities are examined in turn until one exceeds u. algorithm poisson random number (Knuth).

    init:
         Let L ← e−λ, k ← 0 and p ← 1.
    do:
         k ← k + 1.
         Generate uniform random number u in [0,1] and let p ← p × u.
    while p > L.
    return k − 1.

1969

• (Knuth, 1969) ⇒ Donald E. Knuth. (1969). Seminumerical Algorithms. The Art of Computer Programming, Volume 2. Addison Wesley.

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