On Choosing Optional Distributions in Case of Poor Fit of a Discrete Data to Poisson Distribution Especially at the Tails

The testing of the goodness of fit of a data to a Poisson distribution through the Poissonness plot is an interesting way to obtain a visual standpoint of the issue. Based on a real data from the said distribution, the paper discusses how the plot can be used to detect the lack of fit of the data, especially at the right tail of the Poisson distribution. In such a case, the generalized Poisson distribution (both Type I and Type II) or compound distribution may be considered as a better option