Abstract
This article introduces a new distribution with two tuning parameters specified on the unit interval. It follows from a 'hyperbolic secant transformation' of a random variable following the Weibull distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions over the unit interval is a motivation for the study. The main distributional structural properties of the new distribution are established. The different estimation methods and two simulation works have been derived for model parameters. Subsequently, we develop a related quantile regression model for further statistical perspectives. We consider two real data applications based on the educational measurements of both OECD and some non-members of OECD countries. Our regression model aims to relate the desire to get top grades on certain young students in the OECD countries with some of their Education and School Life Index such as reading performance, work environment at home, and paid work experience. It is shown that the elaborated quantile regression model has a better fitting power than famous regression models when the unit response variable possesses skewed distribution as well as two independent variables are significant in the statistical sense at any standard significance level for the median response.