Conway–Maxwell–Poisson distribution

URI: https://gptkb.org/entity/Conway–Maxwell–Poisson_distribution
GPTKB entity
Statements (27)
Predicate Object
gptkbp:instanceOf gptkb:organization
gptkbp:alsoKnownAs gptkb:COM-Poisson_distribution
gptkbp:application biostatistics
ecology
marketing
queueing theory
actuarial science
traffic modeling
gptkbp:citation gptkb:Conway,_J._H.;_Maxwell,_W._L._(1962)._'A_queuing_model_with_state_dependent_service_rates.'_Journal_of_Industrial_Engineering.
gptkbp:generalizes gptkb:Poisson_distribution
gptkbp:hasModel over-dispersed count data
under-dispersed count data
https://www.w3.org/2000/01/rdf-schema#label Conway–Maxwell–Poisson distribution
gptkbp:introducedIn 1962
gptkbp:namedAfter gptkb:John_Horton_Conway
gptkb:William_L._Maxwell
gptkbp:normalizationConstant Z(lambda, nu) = sum_{j=0}^∞ (lambda^j)/(j!)^nu
gptkbp:parameter lambda
nu
gptkbp:probabilityMassFunction P(X=k) = (lambda^k) / (k!)^nu * 1/Z(lambda, nu)
gptkbp:reduces Bernoulli distribution when nu→∞
Poisson distribution when nu=1
geometric distribution when nu=0, lambda<1
gptkbp:supports non-negative integers
gptkbp:usedFor modeling count data
gptkbp:bfsParent gptkb:John_Horton_Conway
gptkbp:bfsLayer 5