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Poisson Distribution

  The Poisson distribution can be defined as the limiting case of the binomial distribution for but = const. It thus describes the behaviour of a large number n of independent experiments of which only a very small fraction pn is expected to yield events of a given type A. As an example, n may be the number of radioactive nuclei in a source and p the probability for a nucleus to decay in a fixed interval of time. The probability for X=k events of type A to occur is

The distribution has the following properties

If k events are observed, is an unbiased estimator of the single parameter . The variance of is also equal to , hence approximately equal to

A simple generator for random numbers taken from a Poisson distribution is obtained using this simple recipe: if is a sequence of random numbers with uniform distribution between zero and one, k is the first integer for which the product .

Rudolf K. Bock, 7 April 1998