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The Skellam distribution is a discrete probability distribution related to the difference between two independent Poisson-distributed random variables. It has been used in a variety of contexts, including sports or supply and demand imbalances in shared transportation. Stata does not support the Skellam distribution or Skellam regression. We present a command, skellamreg, to estimate the parameters of a Skellam distribution and Skellam regression model using Mata’s optimize function.
Verardi et al. (Sat,) studied this question.