This paper proposes an extension of zero-inflated models for analyzing rounded counting outcomes. A zero-inflated mixture of power series is proposed, and the EM algorithm is developed to estimate parameters. The accuracy of estimators is evaluated using a simulation study. The results of simulations show that the estimation procedure is successful and estimates are accurate. An application of our models for analyzing the number of cigarettes smoked per day of respondents for the American's Changing Lives study is enclosed. The proposed model best fits the data and the relationships between rounded counts and other covariates revealed by proposed regression models.
