On the arcsecant hyperbolic normal distribution. Properties, quantile regression modeling and applications

Abstract

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.