The weighted hyper-Poisson model for overdispersed and underdispersed situations

{A weighted version of the hyper-Poisson distribution is developed to modelling overdispersed and underdispersed datasets, and its use is illustrated with the help of real-life applications.} In this paper, we consider a particular form of a weighted version of the hyper-Poisson distribution for modelling overdispersed and underdispersed count data and study some of its important statistical aspects, including the derivation of the expressions for raw moments, factorial moments, mean and variance. We also obtain the recursion formulae for probabilities, raw moments and factorial moments of the proposed weighted model. We discussed the estimation of the parameter of the proposed model using the method of maximum likelihood and constructed test procedures for testing the significance of the additional parameter. Moreover, we illustrate the procedures with the help of two real-life datasets and show that the proposed weighted model gives better fit to the datasets than the existing models. A brief simulation study is also carried out for assessing the efficiency of the maximum likelihood estimators of the parameters of the model.