  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.
