  In directional statistics, the von Mises distribution is a key element in the
analysis of circular data. While there is a general agreement regarding the
estimation of its location parameter $\mu$, several methods have been proposed
to estimate the concentration parameter $\kappa$. We here provide a thorough
evaluation of the behavior of 12 such estimators for datasets of size $N$
ranging from 2 to 8\,192 generated with a $\kappa$ ranging from 0 to 100. We
provide detailed results as well as a global analysis of the results, showing
that (1) for a given $\kappa$, most estimators have behaviors that are very
similar for large datasets ($N \geq 16$) and more variable for small datasets,
and (2) for a given estimator, results are very similar if we consider the mean
absolute error for $\kappa \leq 1$ and the mean relative absolute error for
$\kappa \geq 1$.
