On zero-inflated mixed Poisson transmuted exponential distribution: Properties and applications to observation with excess zeros

Zero-inflated distributions are assumed when count observations are characterised by an excess frequency of zero. This study utilises the cubic rank transmutation map to extend the exponential distribution and obtain a new mixing distribution. The distribution is then used to obtain a new mixed Poisson distribution and its zero-inflated form. Different momentbased mathematical properties of the mixed Poisson distributions and their zero-inflated forms are presented. Five count data sets with varying percentages of zero counts are assessed with new propositions and with both Poisson and negative binomial distributions (along with their respective zero-inflated forms). Performance is compared using both -2LL and chi-square goodness of fit. The new proposition outperforms both Poisson and negative binomial distributions (and their zero-inflated forms). Results also reveal that zero-inflated forms of the new proposition are inferior to their classical form. In most cases the classical negative binomial distribution also provides a better fit than its zero-inflated form while the zeroinflated Poisson distribution outperforms the Poisson distribution. In conclusion, most mixed Poisson distributions exhibit the ability to effectively model the observations with excess zero and tend to provide a better fit to the count observations with excess zero than their zeroinflated forms.