English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Characterizations of distributions is an important part of distribution theory which has attracted the attention of a good number of researchers in applied sciences, where an investigator is interested to know if their model follows the right distribution. Therefore the investigator relies on conditions under which their model would follow specifically the chosen distribution. Altun(2019) introduced a new discrete probability model called New Poisson-Weighted Exponential (NPWE) distribution and argued that such a distribution is needed in the case of over-dispersed data sets. Famoye(2019) proposed a discrete distribution called Exponentiated Weibull-Geometric (EWG) which, in part, deals with the under-dispersed or over-dispersed count data. In this short note, we present certain characterizations of NPWE and EWG distributions based on: (i) the conditional expectation of certain function of the random variable for NPWE and EWG and (ii) in terms of the reversed hazard function for EWG. The main goal here is to complete, in some way, the works of Altun and Famoye. The cumulative distribution function (cdf), F (x), thecorresponding probability mass function (pmf), f (x), the hazard function, hF (x) and the reversed hazard function rF (x) of the NPWE distribution are given, respectively, by

Characterizations of the New Poisson-Weighted Exponential and the Exponentiated Weibull-Geometric Discrete Distributions