  A class of discrete distributions can be derived from stationary renewal
processes. They have the useful property that the mean is a simple function of
the model parameters. Thus regressions of the distribution mean on covariates
can be carried out and marginal effects of covariates calculated. Probabilities
can be easily computed in closed form for only two such distributions, when the
event interarrival times in the renewal process follow either a gamma or an
inverse Gaussian distribution. The gamma-based distribution has more attractive
properties and is described and fitted to data. The inverse-Gaussian based
distribution is also briefly discussed.
