Models for zero-inflated count data using the Neyman type A distribution

We explore the possibility of modelling zero-inflated count data using the Neyman type A distribution. We extend three parameterizations of the Neyman type A distribution to allow their parameters to depend on covariates. We develop models which relate counts of Leadbeater's possum to various habitat variables to illustrate the methodology. Half-normal plots are constructed for each model to explore the quality of the fit. We then formally compare the Neyman type A models using the method of Cox to test non-nested hypotheses. Finally, we compare each of the Neyman type A models with a model from a competing family, the conditional Poisson model.