Weighted negative binomial distribution: properties and applications

Here we consider a weighted version of the negative binomial distribution and illustrate its usefulness through fitting Covid-19 datasets. We obtain several important properties of the distribution such as probability generating function, cumulative distribution function, survival and hazard rate functions, as well as expressions for factorial and raw moments, and recurrence relations for probabilities. Further we discuss the estimation of the parameters of the model and constructed certain test procedures for examining the significance of the parameter. A simulation study is carried out for assessing the performance of the estimators of the parameters of the model obtained through the method of maximum likelihood.