Some mechanisms leading to underdispersion: Old and new proposals

Abstract 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.