Frequent and recurrent ventricular premature beats (VPB's) are considered to be associated with a higher risk of sudden cardiac death, particularly for survivors of myocardial infarction (MI). The distribution of VPB's has a large probability mass at zero, and a very heavy right hand tail. In this research, we fitted a model to VPB for patients for which VPB was present. The model was fitted on the basis of a relatively large data set on MI survivors in Israel. The model was fitted by a method which is based on the generalized linear model. This method, which was introduced by Zeger and Liang, is designed for longitudinal data and uses the quasi-likelihood concept. No specific assumptions are required on the shape of the distribution of the dependent variable. The results indicate that the model fits the data quite well but underestimates the very extreme high values. This research demonstrates the applicability of generalized linear models for longitudinal non-Gaussian data. Such data often arise in medical studies. The study also points out the distributional properties of VPB counts. In particular, it shows their associations with simple clinical and epidemiological variables, and with certain time periods during the day.