Abstract
MirMostafaee et al. (2019) proposed a continuous univariate distribution called Exponentiated Generalized Power Lindley (EGPL) distribution and studied certain properties and applications of their distribution. Akdogan et al. (2019) introduced a discrete distribution called Geometric-Zero Truncated Poisson (GZTP) distribution and provided its properties and applications. The present short note is intended to complete, in some way, the works cited above via establishing certain characterizations of the EGPL and GZTP distributions in different directions.
Highlights
Characterizations of distributions is an important research area which has recently attracted the attention of many researchers
We present our characterizations of Exponentiated Generalized Power Lindley (EGPL) in four subsections
In this subsection we present characterizations of EGPL distribution in terms of a simple relationship between two truncated moments
Summary
Characterizations of distributions is an important research area which has recently attracted the attention of many researchers. This short note deals with various characterizations of EGPL and GZTP distributions to complete, in some way, the works of MirMostafaee et al (2019) and Akdogan et al (2019). These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) the hazard function; (iii) the reverse hazard function and (iv) the conditional expectation of a function of the random variable. One can write down the formulas for the hazard and reverse hazard functions corresponding to these distributions as needed
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