Estimating Skellam distribution and regression parameters in Stata

Abstract

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.