The generalized poisson distribution when the sample mean is larger than the sample variance

The generalized Poisson distribution (GPD), containing two parameters and studied by many researchers, was found to fit data arising in various situations and in many fields. It is generally assumed that both parameters (θ,λ) are non-negative, and hence the distribution will have a variance larger than the mean. However, it appears that the distribution, as a descriptive model, fits many data for negative values of λ, which implies that the mean must be greater than the variance. Thetruncation of the GPD, proposed to remedy the deficiency in the model in this case, is investigated on the basis of the error analysis on the computer and it is suggested that the truncation error for most of the cases is negligible and that the model can be used without any correction for truncation.