A distribution for dependent unit vectors

Abstract

A bivariate generalization of the Fisher-von Mises distribution is introduced. The moments and limiting forms of the new distribution are derived. Then procedures to calculate consistent and efficient estimates of the parameters are proposed. New tests of independence are constructed and a numerical example is presented. A special attention is given to instances where the individual samples are highly clustered since they tend to occur often in applications. For such cases simple approximations to the maximum likelihood estimates and reliable small sample tests of independence are provided.