Generic Count Distributions and Their Zero-Inflated Forms: A Simulation Study

The percentage of zero observations necessitating zero-inflated distributions in count data modelling has been a major issue. The challenge in such a situation is determining when to shift from parent distributions to their zero-inflated versions. In most studies, the performances of parent distributions are assessed with those of their zero-inflated forms. This study conducts simulation studies for the Poisson and the negative binomial distributions and their respective zero-inflated forms. Count data [0, 4] with different percentages of zero counts are simulated using different sample sizes. Both negative log-likelihood and Bayesian information criterion (which considers the number of estimated parameters) are used to assess performance. Results show that the zero-inflated Poisson distribution best suits modelling all forms of data when the negative log-likelihood value is used to assess performance. When the BIC is used, the Poisson distribution gives the best performance for both 10% and 20% zeros, while the ZIP distribution is the best for both 50% and 90% zeros. The NB distribution outperforms the ZINB distribution in all situations. Also, in all cases, the negative binomial performs better than the zero-inflated negative binomial distributions. To further assess the distributions, four count data sets with varying percentages of zero are examined. Both the ZIP and the NB distributions perform better than others.