A model for underdispersed count data

Abstract Underdispersed count data sometimes occurs in economic studies, and is here modelled as a mixture of a Poisson random variate and of one of a new class of underdispersed ‘Poisson $$-m$$ - m ’ distributions. In these distributions, m adjacent Poisson probabilities are summed and relabelled. The mixture is a 2 or 3-parameter distribution. Although designed to model underdispersion, it can can also be moderately overdispersed and can also model bimodality. Probabilities are simple to compute, as are random numbers, and there is a probabilistic basis. Moments can be computed exactly, and there is also a simple asymptotic approximation for the mean and variance valid down to very low counts. Fits to data show the new distributions to be generally superior to two benchmarks, the COM-Poisson and weighted Poisson distributions.