Introducing an Alternative Flexible Bivariate Distribution for Count Data Expressing Data Dispersion

• Activity Number: 41 - Topics on Bayesian Inference
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: IMS
• Author(s): Kimberly Weems* and Kimberly Sellers and Tong Li
• Companies: North Carolina Central Univ and Georgetown University and Georgetown University
• Keywords: bivariate distribution; dispersion; Conway-Maxwell-Poisson; dependence; trivariate reduction

Abstract

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.