A new three-parameter model with support on a bounded domain: Properties and quantile regression model

In this article, we proposed a new three-parameter model with a bathtub failure rate. The main properties of the new model are derived, such as quantile function, moments, the moment of residual life, stress strength reliability parameter, order statistics, extreme value distribution, Shannon entropy, and Renyi entropy. Maximum likelihood estimation (MLE) is considered for the parameter estimation, and the information matrix is obtained. Simulation studies were used to assess the performances of the estimators by discussing their bias, mean square error, confidence interval, and coverage probability. In addition, we discussed the quantile regression model based on the proposed model; we examined the performance of their MLEs by simulation studies via the randomized quantile residuals. Two real data sets are used to illustrate the importance of the new model in practice.