Open Access Open Access  Restricted Access Subscription or Fee Access

On estimation of the probability mass function and the cumulative distribution function of a natural discrete one parameter polynomial exponential distribution

Indrani Mukherjee, Sudhansu S. Maiti, Rama Shanker

Abstract



In this paper, 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 in literature. Maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of the probability mass function (PMF) and the cumulative distribution function (CDF) of the NDOPPE distribution
have been derived. The estimators have been compared with respect to their mean squared errors (MSEs). Simulation study has been conducted to verify the consistency of the estimators. Three real data illustrations have been reported.

Keywords


Goodness of fit; Maximum likelihood estimator; Natural discrete Lindley distribution; Simulation; Uniformly minimum variance unbiased estimator.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.