فهرست نشریات علمی دسترسی آزاد ایران

The Pearson-type family densities are among the most important classes of distributions, also playing key roles in directional statistics. To model data scattered asymmetrically on non-Euclidean spaces, including spheres, the researchers confined themselves to extending particular distributions from the class of the Pearson-type family densities. Those specific distributions are symmetric, but their extended versions are usually heavy-tailed. This paper introduces alternative probability density functions in the class of Pearson-type distributions on the sphere with the spherical Student's t, Fisher, and Chi-square densities as the subfamilies. We show that it is intrinsically asymmetric by investigating various theoretical properties of this new subclass. Intensive simulation studies are conducted to explore various aspects of this subclass. Also, modeling two real-life data using the proposed densities and comparing the results with the fits arising from other common spherical distributions are considered.