No. 1034

Title:

Generalized Laplace distributions on spheres by conditioning normal mixtures

Author(s):

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

Key words:

Directional statistics; von Mises-Fisher distribution; cardioid distribution.

Abstract:

A distribution on a unit sphere is generated by conditioning a mixture of normal distribution when its weight has an inverse gamma distribution. It can be regarded as the generalized (symmetric) Laplace distribution on a unit sphere. The density involves a modified Bessel function of the third kind. This new distribution is approximated by von Mises-Fisher, cardioid and Jones-Pewsey distributions. It is suggested to use EM algorithm to find maximum likelihood estimates of the parameters. thunder of a day.