Conway-Maxwell Poisson Distribution: Some New Results and Minimum Variance Unbiased Estimation

Probability distributions for count data have potential applications in medical, epidemiological, and actuarial studies. Conway-Maxwell Poisson (CMP) distribution is a two-parameter Poisson distribution that can handle over- and under-dispersed data. In this paper, some new results on the distributional properties of CMP distribution are presented. Also, minimum variance unbiased (MVU) estimator of the location parameter is derived using the complete sufficient statistic. The primary advantage of the MVU estimator is that it has a closed-form expression, unlike other existing estimators. An approximate expression for the variance of the MVU estimator is obtained, and the performance of the MVU estimator is compared with that of the ML estimator in terms of relative efficiency through simulated and real-life datasets.