The Unit Folded Normal Distribution: A New Unit Probability Distribution with the Estimation Procedures, Quantile Regression Modeling and Educational Attainment Applications

In this paper, we develop a continuous distribution on the unit interval characterized by of absolute hyperbolic tangent transformation random variable following normal distribution. The lack research prospect transformations providing flexible distributions is motivation for study. First, study it theoretically and discuss its properties interest from modeling point view. particular, shown that proposed accommodates various levels skewness kurtosis. Then, some statistical work performed. We investigate diverse estimation methods involved parameters evaluate their performance through two simulation studies. Subsequently, quantile regression model derived developed. Two real-world data applications are provided. first application about univariate percentage educational attainment countries, which one indicator education topic Better Life Index (BLI) Organization Economic Co-operation Development (OECD) countries. second to explain relationship between countries with work-life balance, safety, health topics BLI via median modeling. For considered sets, models show they have better abilities than competitive under comparison criteria. results also indicate covariates (statistically) significant at any ordinary level significance response.