In this paper, we introduce a new probability distribution defined on the unit interval (0,1), called the unit extended exponential (UEE) distribution. The proposed model is obtained through a transformation of a random variable following the extended exponential distribution, leading to a flexible family able to describe skewed and boundary-concentrated data. The structural properties of this distribution are derived, including its density, cumulative distribution, survival, hazard rate and quantile function, along with the mode and moments. A characterization based on its hazard function is also presented. Parameter estimation is performed via maximum likelihood. Under standard regularity conditions, the asymptotic properties of the estimators are established. A Monte Carlo simulation study is carried out to assess the finite-sample performance of the estimators. Finally, the usefulness of the model is illustrated through two applications to real proportion data, where our proposal is compared with competing models such as the unit-Lindley and Beta distributions using information criteria. The results suggest that the proposed distribution provides a competitive and often superior fit.
Gaete et al. (Wed,) studied this question.
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