ABSTRACT
This chapter gives summary tables and plots for explicit gamlss.dist discrete count distributions. All the distributions have range {0, 1, 2, 3,…}, with the exception of the logarithmic and the Zipf distributions, which have range { 1, 2, 3, …}. There are two parameterizations of the geometric distribution in the gamlss.dist package: GEOM(mean) and GEOMo(mean). The double Poisson distribution is a special case of the double exponential family of Efron. It has approximate mean and approximate variance. The generalized Poisson distribution was derived by Consul and Jain as an approximation of a generalized negative binomial distribution. In recognition of P. C. Consul’s contribution to this distribution, it is sometimes called Consul’s generalized Poisson distribution. In gamlss.dist, a parameterization of the generalized Poisson distribution which is more suitable for regression modeling is used.
