On estimation of the PMF and the CDF of a natural discrete one parameter polynomial exponential distribution

TL;DR

This paper introduces a new discrete distribution called NDOPPE, derived as a mixture of negative binomial distributions, and provides methods to estimate its PMF and CDF, supported by simulations and real data analysis.

Contribution

It proposes the NDOPPE distribution as a novel discrete analog of OPPE, extending the natural discrete Lindley distribution, and derives estimators for its PMF and CDF.

Findings

MLE and UMVUE estimators are derived and compared.

Simulation confirms estimator consistency.

Real data application demonstrates practical utility.

Abstract

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.