Generating Poisson-distributed Random Variables
A simple algorithm to generate random Poisson-distributed numbers (pseudo-random number sampling) has been given by Knuth (see References below):
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 and let p ← p × u. while p > L. return k − 1.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.
Read more about this topic: Poisson Distribution
Famous quotes containing the words random and/or variables:
“Novels as dull as dishwater, with the grease of random sentiments floating on top.”
—Italo Calvino (1923–1985)
“The variables are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.”
—George Steiner (b. 1929)