Extended Conway-Maxwell-Poisson distribution and its properties and applications

A new three parameter natural extension of the Conway-Maxwell-Poisson (COM-Poisson) distribution is proposed. This distribution includes the recently proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty, S. and Ong, S. H. (2014): A COM-type Generalization of the Negative Binomial Distribution, Accepted in Communications in Statistics-Theory and Methods] and the generalized COM-Poisson (GCOMP) distribution [Imoto, T. :(2014) A generalized Conway-Maxwell-Poisson distribution which includes the negative binomial distribution, Applied Mathematics and Computation, 247, 824-834]. The proposed distribution is derived from a queuing system with state dependent arrival and service rates and also from an exponential combination of negative binomial and COM-Poisson distribution. Some distributional, reliability and stochastic ordering properties are investigated. Computational asymptotic approximations, different characterizations, parameter estimation and data fitting example also discussed.Comment: 14 pages, 2 figures, 3 tables, prepreprint, new sections added, new references added,new coauthor adde

A flexible regression model for count data

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive to Poisson regression. We propose a regression model based on the Conway--Maxwell-Poisson (COM-Poisson) distribution to address this problem. The COM-Poisson regression generalizes the well-known Poisson and logistic regression models, and is suitable for fitting count data with a wide range of dispersion levels. With a GLM approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a COM-Poisson regression over a standard Poisson regression. We compare the COM-Poisson to several alternatives and illustrate its advantages and usefulness using three data sets with varying dispersion.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS306 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A flexible distribution class for count data

The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-parameter generalization of the Poisson distribution that can accommodate data over- or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model’s flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion

Count regression models for recreation demand: an application to Clear Lake

An important objective for policy-makers is how to allocate resources for the enjoyment of its citizens. Outdoor recreation is a very popular hobby for a lot of people. The sites they travel to for recreational purposes are public sites such as the Clear Lake, located in central Iowa. The users of the lake often care about the quality of the water. It is the goal of the researcher to determine how much they are willing to pay in order to preserve or improve the water quality. The researcher must decide on not only the theoretical methodology, but the appropriate statistical model. The focus of this thesis is using count data models to estimate individuals\u27 willingness to pay. A common count data model is the Poisson model, however it is restrictive and often alternative models must be used. This thesis introduces a new count data model to the literature: The Conway-Maxwell-Poisson regression model. Using the data gathered by individual users at Clear Lake, I contrast this model with a popular alternate to the Poisson model, the negative binomial model