An Alternative Count Distribution for Modeling Dispersed Observations

Abstract

In most cases, count data have higher variances than means; hence using the Poisson distribution to model such observations is misleading because of the equality of the Poisson mean and variance. This study proposes a new two-parameter mixed Poisson distribution for modeling dispersed count observations. The exponential distribution is transmuted to obtain a new mixing distribution for the new proposition. Different moment-based mathematical properties of the new proposition are obtained. Applications using dispersed count observations with excess zero are made. Comparisons with related distributions for modeling dispersed observation reveal that the new distribution performs creditably well.