Discipline: Mathematics & Statistics
Subcategory: STEM Research
Kimberly Weems - North Carolina Central University
Co-Author(s): Kimberly F. Sellers, Georgetown University, Washington, DC
The bivariate Poisson distribution is a natural choice for modeling bivariate count data. Its constraining assumption, however, limits model flexibility in some contexts. Sellers et al. (2016) developed a bivariate Conway-Maxwell-Poisson (CMP) distribution based on the compounding method that includes the bivariate Poisson, bivariate Bernoulli, and bivariate geometric distributions as special cases. The construct, however, produces marginal forms that are not easily understood in relation to a general dispersion level. This work instead considers the trivariate reduction method to develop an alternate bivariate CMP distribution. Accordingly, this approach produces marginals that have a flexible form which includes several special case distributions for certain parameters. As a result, this bivariate CMP model is another flexible distribution for modeling bivariate count data containing data dispersion.
Funder Acknowledgement(s): This research was partially supported by the National Science Foundation Grant 1700235.
Faculty Advisor: None Listed,