Bayes estimation of a langevin mean direction

ABSTRACT

A Langevin distribution with two parameters (mean direction and concentration parameter) has been extensively used for modeling and analyzing problems related to directional data. In this article, we examine the estimation problem for the mean direction. Bayes estimators are derived with respect to a conjugate as well as the Jeffreys’ priors. Further in case of unknown concentration parameter, other priors are also chosen. An extensive analysis of risk behavior of Bayes estimators is carried out with the help of simulations.

KEYWORDS:

• Admissibility
• Bayes estimator
• Directional data
• Risk analysis

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H11
• Secondary 62F15
• 62C15