On estimation of the PMF and the CDF of a natural discrete one parameter polynomial exponential distribution
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In this article, a new natural discrete analog of the one parameter polynomial exponential(OPPE) distribution as a mixture of a number of negative binomial distributions has been proposed and is called as a natural discrete one parameter polynomial exponential (NDOPPE) distribution. This distribution is a generalized version of natural discrete Lindley (NDL) distribution, proposed and studied by Ahmed and Afify (2019). Two estimators viz., MLE and UMVUE of the PMF and the CDF of a NDOPPE distribution have been derived. The estimators have been compared with respect to their MSEs. Simulation study has been conducted to verify the consistency of the estimators. A real data illustration has been reported.
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