Modelling Count Variables: A Comparative Analysis of two Discretization Techniques

Background: Different discretization methods have been proposed to provide a better fit to count observations with characteristics resembling a given continuous distribution. This is done to provide discrete distribution with characteristics resembling a chosen continuous distribution. This study compares discretization through survival function and mixed Poisson processes.

Methodology: The Ailamujia distribution is extended using the cubic rank transmutation map. The shapes and some moment based properties of the continuous distribution are obtained. Two discretized versions of the distribution obtained are unimodal and skewed, depicting characteristics of the continuous distribution. Parameters of the new discrete distributions are estimated using the method of maximum likelihood, and both AIC and chi-square are used for model comparison.

Results: Real-life assessment using five count data shows that the two propositions provide a better fit than the three competing distributions considered. Also, discretization through the mixed Poisson process offers a better fit than the survival function technique.

Conclusion: Various moment-based mathematical properties of the discretization through the mixed Poisson process are easily obtainable and hence, can be easily characterized.