On the Versatility of the Unit Logistic Exponential Distribution: CapturingBathtub, Upside-Down Bathtub, and Monotonic Hazard Rates

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.