A New One-Parameter Size-Biased Poisson Distribution for Modelling Underdispersed Count Data

Abstract

This paper proposes a new one-parameter discrete distribution for positive count data, named underdispersed size-biased Poisson distribution, as an alternative to modeling underdispersed positive count data. Several properties and measures are presented, such as moments about origins, variance, skewness, kurtosis, index of dispersion, coefficient of variation, and recurrence relationship. Estimators are also developed based on two estimation techniques, i.e., maximum likelihood and moment method. It was found that both estimation techniques yield an identical estimator, which is unique, positively biased, consistent, and asymptotically normal. Finally, a dataset is fitted to the proposed distribution to verify the ability of the proposed distribution to explain the real dataset with a comparison to two known size-biased distributions.