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In this paper, a reduced one-parameter contagious distribution was developed from the joint distribution of three-parameter gamma and Poisson distributions, on which Lakshmi’s three-parameter gamma distribution is based to model a count data. The distribution properties and some common descriptive measures relating to this contagious distribution are derived. The behavior of the probability mass function with changes in parameters was also studied. The parameter estimation by the maximum likelihood and moment-generating function methods is discussed. A simulation study was carried out with the proposed model to check for consistency and bias. The new model show consistency as the sample size increases. The model was applied to a real-life dataset and was seen to be more flexible in capturing excess zero, under, and over-dispersion in count data and proved to be a useful alternative to some existing zero-inflated models.
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