A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution

Galit Shmueli, Thomas P. Minka, Joseph B. Kadane, Sharad Borle and Peter Boatwright

Journal of the Royal Statistical Society Series C, 2005, vol. 54, issue 1, 127-142

Abstract: Summary. A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two‐parameter extension of the Poisson distribution that generalizes some well‐known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway–Maxwell–Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway–Maxwell–Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway–Maxwell–Poisson distribution in fitting count data which do not seem to follow the Poisson distribution.

Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (74)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9876.2005.00474.x

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssc:v:54:y:2005:i:1:p:127-142

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9876

Access Statistics for this article

Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith

More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().