In this paper, a unit logistic exponential (ULE) distribution is proposed. The ULE distribution appears to be more flexible than some of the existing well-known univariate distributions defined on the unit interval due to its five failure rate shapes, i.e. bathtub and upside-down bathtub, decreasing, increasing and constant shapes. Some statistical properties of the ULE distribution have been discussed. The quantile regression analysis is conducted. A simulation study has been conducted to check the consistency of the adopted MLE procedure. Three real-life data sets have been used to compare the ULE distribution with some existing distributions and the ULE distribution performs best fit among all.
Saboor et al. (Thu,) studied this question.