Scientists and engineers use Poisson's probability distribution to characterize the statistics of counts for improbable events whose average number is small. My article in the May/June 2001 issue of Computing in Science and Engineering describes interesting properties of this distribution.

    The main topics I discuss are how the Poisson distribution relates to the binomial and Gauss (normal) distributions, the comparative statistics of the three distributions, sums and differences of Poisson-distributed random variables, and computing Poisson-distributed random numbers. There are references to sources, including my Atlas for Computing Mathematical Functions (Wiley, 1997), which includes descriptions of 20 probability distributions by figures and C or Fortran-90 programs.

    Most of the description in the Poisson Distributions article is pictorial, using figures made by Mathematica, a system for doing mathematics by computer. If you have access to Mathematica, copy the notebook from this web (its size is less than 60 Kbyte) and explore the distribution yourself. The six figures you obtain should be just like the figures in the article. After that check, vary the parameters in the calculations to improve your understanding of Poisson distributions.

Note: Reference 3 should be to CiSE Sept./Oct. 1999, not 2000.