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- Conway–Maxwell–Poisson_distribution abstract "In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion. It is a member of the exponential family, has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case.The COM-Poisson distribution was originally proposed by Conway and Maxwell in 1962 as a solution to handling queueing systems with state-dependent service rates. The probabilistic and statistical properties of the distribution were published by Shmueli et al. (2005).The COM-Poisson is defined to be the distribution with probability mass functionfor x = 0,1,2,... , and ≥ 0,whereThe function serves as a normalization constant so the probability mass function sums to one. Note that does not have a closed form.The additional parameter which does not appear in the Poisson distribution allows for adjustment of the rate of decay. This rate of decay is a non-linear decrease in ratios of successive probabilities, specificallyWhen , the COM-Poisson distribution becomes the standard Poisson distribution and as , the distribution approaches a Bernoulli distribution with parameter . When the CoM-Poisson distribution reduces to a geometric distribution with probability of success provided .For the COM-Poisson distribution, moments can be found through the recursive formula".
- Conway–Maxwell–Poisson_distribution wikiPageID "15845763".
- Conway–Maxwell–Poisson_distribution wikiPageRevisionID "604304965".
- Conway–Maxwell–Poisson_distribution char "Not listed".
- Conway–Maxwell–Poisson_distribution entropy "Not listed".
- Conway–Maxwell–Poisson_distribution kurtosis "Not listed".
- Conway–Maxwell–Poisson_distribution median "No closed form".
- Conway–Maxwell–Poisson_distribution mgf "Not listed".
- Conway–Maxwell–Poisson_distribution mode "Not listed".
- Conway–Maxwell–Poisson_distribution name "Conway–Maxwell–Poisson".
- Conway–Maxwell–Poisson_distribution skewness "Not listed".
- Conway–Maxwell–Poisson_distribution type "mass".
- Conway–Maxwell–Poisson_distribution subject Category:Discrete_distributions.
- Conway–Maxwell–Poisson_distribution subject Category:Poisson_processes.
- Conway–Maxwell–Poisson_distribution subject Category:Probability_distributions.
- Conway–Maxwell–Poisson_distribution comment "In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion.".
- Conway–Maxwell–Poisson_distribution label "Conway–Maxwell–Poisson distribution".
- Conway–Maxwell–Poisson_distribution label "Loi de Conway-Maxwell-Poisson".
- Conway–Maxwell–Poisson_distribution sameAs Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution.
- Conway–Maxwell–Poisson_distribution sameAs Loi_de_Conway-Maxwell-Poisson.
- Conway–Maxwell–Poisson_distribution sameAs Q3258310.
- Conway–Maxwell–Poisson_distribution sameAs Q3258310.
- Conway–Maxwell–Poisson_distribution wasDerivedFrom Conway–Maxwell–Poisson_distribution?oldid=604304965.