t-distributions on Some Manifolds

Abstract

Student's t-distribution appears as a sampling distribution in the interval estimation or test of a normal mean with unknown variance. In addition, it provides a more flexible model than a normal distribution when a theoretical distribution is fitted to a data set. On spheres a symmetric t-distribution is constructed by Shimizu and Iida (2002). In this talk we propose (skew) t- distributions on the circle, on the complex sphere, and on the cylinder. The main point is: Proposed t-distributions converge to the corresponding 'normal' distributions as degrees of freedom tend to infinity. Details can be seen in the paper by Kato and Shimizu (2004).