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Abstract:
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Negative Hypergeometric distribution is considered as a waiting time distribution when drawing sample without replacement from a finite population. It is analogous to the Negative Binomial distribution, when sampling with replacement from an infinite population. We propose a modified version of the negative hypergeometric distribution called the COM-Negative Hypergeometric distribution (COM-NH). It is shown that under some limiting conditions, COM-NH approaches to a distribution that we call COM-Negative Binomial Distribution (COM-Neg.B).These new distributions approach to COM-Poisson distribution (Conway and Maxwell,1962) under suitable limiting conditions. For the proposed model we have also developed statistical inference for analyzing some existing data sets and compare the results obtained with other models. We have investigated some properties such as bias, MSE, and coverage probabilities of the maximum likelihood estimator for the parameters of COM-NH and COM-Neg.B by simulation. We have developed likelihood Ratio test and score type tests to test the underlying model is COM-NH or COM-Neg.B as opposed to their ordinary counterparts, also investigated power of these tests.
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