New Class of Spherical Pearson Type Family Distributions to Model
Asymmetric Spherical Data
Abstract
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.