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On the existence of maximum likelihood estimates for the parameters of the Conway-Maxwell-Poisson distribution.
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- المؤلفون: Bedbur, Stefan1 ; Kamps, Udo1 ; Imm, Anton1
- المصدر:
ALEA. Latin American Journal of Probability & Mathematical Statistics. 2023, Vol. 20 Issue 1, p561-575. 15p.
- الموضوع:
- معلومة اضافية
- نبذة مختصرة :
As a well-known and important extension of the common Poisson model with an additional parameter, Conway-Maxwell-Poisson (CMP) distributions allow for describing under- and overdispersion in discrete data. Constituting a two-parameter exponential family, CMP distributions possess useful structural and statistical properties. However, the exponential family is not steep and maximum likelihood estimation may fail even for non-trivial data sets, which is different from the Poisson case, where maximum likelihood estimation only fails if all data outcomes are zero. Conditions are examined for existence and non-existence of maximum likelihood estimates in the full family as well as in subfamilies of CMP distributions, and several figures illustrate the problem. [ABSTRACT FROM AUTHOR]
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