This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.
In this paper, we develop a continuous distribution on the unit interval characterized by the distribution of the absolute hyperbolic tangent transformation of a random variable following the normal distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions on the unit interval is a motivation for the study. First, we study it theoretically and discuss its properties of interest from a modeling point of view. In particular, it is shown that the proposed distribution accommodates various levels of skewness and kurtosis. Then, some statistical work is performed. We investigate diverse estimation methods for the involved parameters and evaluate their performance through two simulation studies. Subsequently, the quantile regression model derived from the proposed distribution is developed. Two real-world data applications of interest are provided. The first application is about the univariate modeling of the percentage of the educational attainment of some countries, which is one indicator of the education topic of the Better Life Index (BLI) of the Organization for Economic Co-operation and Development (OECD) countries. The second application is to explain the relationship between the percentage of educational attainment of some countries with one indicator of the work-life balance, safety, and health topics of BLI via median quantile regression modeling. For the considered data sets, the proposed distribution and quantile regression models show that they have better modeling abilities than competitive models under some comparison criteria. The results also indicate that covariates are (statistically) significant at any ordinary level of significance for the median response.
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