New Class of Spherical Pearson Type Family Distributions to Model Asymmetric Spherical Data
The Pearson type family densities are among the most important classes of distributions that play a key role in the directional statistics. Their particular structures make them suitable candidates to analysis data on non-Euclidean space, such as sphere. To model data scattered asymmetrically on such spaces, the researchers confined themselves to extend particular distributions from the class of the Pearson type family densities. Those specific distributions are symmetric in nature but their extended versions are usually heavy tailed. In this paper, we introduce some alternative probability density functions in the class of Pearson type distributions on the sphere having the spherical Student’s $t$, Fisher and Chi-square densities as the subfamilies. Via investigating various theoretical properties of this new subclass, we show that it is inheritably asymmetric. To further evaluating this subclass, some simulation studies are conducted. Also, modeling of two real-life data using the proposed densities and then comparing their fitting consequences with those resulted from invoking other common spherical distributions are considered.