Remarks on a parameter estimation for von Mises--Fisher distributions

TL;DR

This paper identifies and corrects an error in the proof of a key result related to parameter estimation for von Mises--Fisher distributions, providing a corrected and alternative proof.

Contribution

It rectifies a mistake in prior work and offers a new, concise proof for the main result on parameter estimation in von Mises--Fisher distributions.

Findings

Corrected the proof of the main theorem

Provided an alternative, shorter proof

Clarified the theoretical foundation for parameter estimation

Abstract

We point out an error in the proof of the main result of the paper of Tanabe et al. (2007) concerning a parameter estimation for von Mises--Fisher distributions, we correct the proof of the main result and we present a short alternative proof.