No. 1035

Title:

Asymmetric t-type distribution on circles

Author(s):

Siew, Hai-Yen (The Graduate University for Advanced Studies);

Kato, Shogo (The Graduate University for Advanced Studies);
Shimizu, Kunio (Keio University)

Key words:


Directional statistics; generalized von Mises distribution; cardioid distribution.

Abstract:


An extended version of t-distribution on the unit circle is generated by conditioning a scale mixture of normals, which is broaden to include not only unimodaliy and symmetry, but also bimodality and asymmetry, depending on the values of parameters. After reparametrization, the distribution contains four circular distributions as special cases: symmetric Jones-Pewsey, generalized von Mises, asymmetric cardioid and asymmetric wrapped Cauchy distributions. As an illustrative example, the proposed model is fitted to the number of the occurrences of thunder of a day.