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In this study, a new three-parameter mixed Poisson Cubic Rank Transmuted New Weighted Exponential Distribution is proposed. The new discrete distribution is obtained by mixing the Poisson distribution with a newly obtained Cubic Rank Transmuted New Weighted Exponential Distribution. Various shapes and mathematical properties of both mixing distribution and the new count distribution are examined. Special cases of the new proposition are also identified. The distribution along with its special cases and other count distributions are assumed for skewed and dispersed count observations. The maximum likelihood estimation is used to provide estimates for the parameters of all examined distributions. Results show that the new proposition along with some of its special cases provide good fit for all the examined data.
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