Poisson distribution

After French mathematician Siméon Denis Poisson (1781-1840), who introduced the distribution in his 1837 work Recherches sur la probabilité des jugements en matière criminelle et en matière civile ("Research on the Probability of Judgements in Criminal and Civil Matters"), although prior work had been done by Abraham de Moivre.

Poisson distribution (plural Poisson distributions)

1. (statistics) Any of a class of discrete probability distributions that express the probability of a given number of events occurring in a fixed time interval, where the events occur independently and at a constant average rate; describable as a limit case of either binomial or negative binomial distributions.
   • 1993, Rolf-Dieter Reiss, A Course on Point Processes, Springer, page 62:

     For the modeling of many phenomena there is a need for enlarging the family of Poisson distributions. One possibility of doing this is the use of mixed Poisson distributions (outlined above).

   • 2000, Michael C. Fleming, Joseph G. Nellis, Principles of Applied Statistics: An Integrated Approach Using MINITAB and Excel, 2nd edition, Thomson, page 116:

     It is worth noting, therefore, that unlike the binomial distribution in which we are interested in observing both 'success' and 'failure', the application of the Poisson distribution is concerned only with occurrences rather than non-occurrences.

   • 2007, “4: Order Statistics for Decoding of Spike Trains”, in Kenji Doya, Shin Ashii, Alexandre Pouget, Rajesh P. N. Rao, editors, Bayesian Brain: Probabilistic Approaches to Neural Coding, The MIT Press, page 83:

     A mixture of Poisson processes will have a spike count described by a mixture of Poisson distributions. A model allowing a mixture of a few Poisson distributions adds substantial flexibility, while keeping the calculations reasonably simple.

   • 2017, William Q. Meeker, Gerald J. Hahn, Luis A. Escobar, Statistical Intervals: A Guide for Practitioners and Researchers, 2nd edition, Wiley, page 128:

     As indicated, problems involving the number of occurrences of independent, randomly occurring events per unit of space or time can often be modeled with the Poisson distribution.

• Poisson process

• exponential distribution