Some mechanisms leading to underdispersion: Old and new proposals

In statistical modeling, it is important to know the mechanisms that cause underdispersion. Several mechanisms that lead to underdispersed count distributions are revisited from new perspectives, and new ones are introduced. These include procedures based on the number of arrivals in arrival processes, such as renewal and pure birth processes and steady-state distributions of birth-death processes, like queues with state-dependent service rates. Weighted Poisson and other well-known underdispersed distributions are also related to birth-death processes. Classical and variable binomial thinning mechanisms are also viewed as important procedures for generating underdispersed distributions, which can also generate bivariate count distributions with negative correlation. Some example applications are shown, one of which is related to Biodosimetry.

Automated summary

In statistical modeling, understanding the mechanisms that cause underdispersion is crucial. This article revisits several mechanisms that lead to underdispersed count distributions from new perspectives, and introduces new ones. These mechanisms include arrival processes, birth-death processes, and thinning mechanisms, which can generate underdispersed distributions with negative correlation. The article also provides example applications, including one related to Biodosimetry.