In
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
and
statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a
discrete probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
named after
Richard W. Conway
Richard Walter Conway (born December 12, 1931) is an American industrial engineer and computer scientist who is the Emerson Electric Company Professor of Manufacturing Management, Emeritus in the Johnson Graduate School of Management at Cornell U ...
,
William L. Maxwell, and
Siméon Denis Poisson
Baron Siméon Denis Poisson FRS FRSE (; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electr ...
that generalizes the
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known ...
by adding a parameter to model
overdispersion
In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model.
A common task in applied statistics is choosing a parametric model to fit a g ...
and
underdispersion
In statistics, overdispersion is the presence of greater variability ( statistical disper