On the Estimation of the Relative Incident Parameter of Negative Multinomial Distribution

Abstract

Oftentimes, the sample sizes are fixed and this always make it possible for one to model a particular distribution for any given data. However, there are some situations that restrict our sampling plan. In this research work, we considered Negative Multinomial sampling in which the sample sizes are not fixed and the observed cell counts are positively correlated. Our interest is to deduce means of estimating the shape parameter of this distribution. We show that Maximum Likelihood Estimate for the shape parameter does not exit, but another means of estimating shape parameter based on the methods of moment estimation and modified chi square statistic. Lastly we observed that the incident rate of any unusual situations could be estimated with this parameter under study.