The inverse trinomial distribution and its application in modeling over-dispersed count Data

In this paper, we apply the inverse trinomial distribution with parameters (p, q, λ) to count data exhibiting over-dispersion. We compare results for the mean parameterized inverse trinomial and the parameter λ as linear predictors in the generalized linear model case. Our results also demonstrate methods for obtaining the means and variances for the zero-inflated and zero-truncated inverse trinomial distributions. Results obtained here indicate that the generalized Poisson type II has a close relationship with the inverse trinomial distributions. Several data examples are employed in this paper for both frequency and data having covariates cases. SAS PROC NLMIXED is employed using adaptive Gaussian quadrature and the Newton-Raphson as the optimizer.