A New Class of Spherical Pearson-type Family of Distributions

Document Type : Original Article

Authors
Meisam Moghimbeygi 1
Mousa Golalizadeh 2
1 Department of Mathematics, Faculty of Mathematics and Computer Science, Kharazmi University, Tehran, Iran
2 Department of Statistics, Tarbiat Modares University, Tehran, Iran
10.22034/jirss.2023.1996191.1004
Abstract
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.
Keywords
Asymmetric Property
Gaussian Hypergeometric Function
Heavy-tailed Distributions
Pearson type Family
Spherical Densities
Subjects
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Journal of the Iranian Statistical Society
Volume 22, Issue 1
June 2023
Pages 99-121

  • Receive Date 14 March 2023
  • Revise Date 11 October 2023
  • Accept Date 29 October 2023