Some additional facts about the unit-Gompertz distribution

In this article, a two-parameter model called unit-Gompertz is studied over the unit interval. We describe its statistical characteristics such as uncertainty measures of Shannon, Tsallis, Renyi, Mathai-Houbold, Kumar and Verma, order statistics, quantile function, maximum likelihood estimation, factorial and characteristic function, moment generating function, and stress-strength analysis. The effectiveness of the studied model is demonstrated by the use of two datasets from the real life. The model has flexible hazard rate shapes, presents better performance and fits the data better than other usual models.