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There are not many known distributions for modeling discrete data. In this paper, we shall introduce a new count data model, which is obtained by compounding two parameter discrete Inverse Weibull distribution with Minimax distribution. The proposed model has several properties such as it can be nested to different compound distributions on specific parameter settings. We shall first study some basic distributional and moment properties of the new distribution. Then, certain structural properties of the distribution such as its unimodality, hazard rate behavior and index of dispersion are discussed. Finally, real data set is analyzed to investigate the suitability of the proposed distribution in modeling count data from medical genetics.

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