This article introduces a new discrete distribution for nonzero count data. Some distributional properties, such as shape, probability generating function, moment generating function, and raw moments, are studied. The maximum likelihood method is applied to estimate the distribution parameters. A nonzero count regression model based on the proposed distribution is developed. The performance of the proposed distribution and its regression model are shown through real nonzero count data, which shows that they outperform other competitive models. Therefore, the proposed model can be considered for count data excluding zero.
