Title: A Note on Inverse Stereographic Projection of Elliptical Distributions

Author(s): Jean-Luc Dortet-Bernadet and Nicolas Wicker
Issue: Volume 80 Series A Part 1 Year 2018
Pages: 138 -- 151
This note concerns a family of distributions on the unit sphere obtained by inverse stereographic projection of elliptical distributions. We give some properties of these distributions with emphasis on the study of unimodality. This construction encompasses many known families of distributions on the unit sphere. Finally we show that it is possible to define new families of unimodal distributions that allow anisotropy.
AMS (2000) subject classification. Primary 62H11; Secondary 62H05.
Keywords and phrases: Inverse stereographic projection, Sphere, Hypersphere, Unimodality, Elliptical distributions