Some More Properties of the Unit-Gompertz Distribution

TL;DR

This paper corrects errors in the initial study of the unit-Gompertz distribution, explores its properties, and examines its reliability measures and stochastic orderings, enhancing understanding of its potential applications.

Contribution

It provides corrections to previous work on the unit-Gompertz distribution and investigates its properties, reliability measures, and stochastic orderings.

Findings

Corrected previous errors in the distribution's properties

Analyzed reliability measures of the distribution

Explored stochastic orderings related to the distribution

Abstract

In a recent paper, Mazucheli et al. (2019) introduced the unit-Gompertz (UG) distribution and studied some of its properties. It is a continuous distribution with bounded support, and hence may be useful for modelling life-time phenomena. We present counter-examples to point out some subtle errors in their work, and subsequently correct them. We also look at some other interesting properties of this new distribution. Further, we also study some important reliability measures and consider some stochastic orderings associated with this new distribution.