# Poisson Random Variable

Jump to navigation
Jump to search

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

## 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)*.

- A simple algorithm to generate random Poisson-distributed numbers (pseudo-random number sampling) has been given by Knuth (Knuth, 1969):

init:LetL ←e^{−λ}, k ← 0 and p ← 1.do: k ← k + 1. Generate uniform random number u in [0,1] andletp ← p × u.whilep > L.returnk − 1.

### 1969

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