Estimating the concentration parameter of a von Mises distribution: a systematic simulation benchmark

In directional statistics, the von Mises distribution is a key element in analysis of circular data. While there general agreement regarding estimation its location parameter μ, several methods have been proposed to estimate concentration κ. We here provide thorough evaluation behavior 12 such estimators for datasets size N ranging from 2 8192 generated with κ 0 100. detailed results as well global results, showing that (1) given κ, most behaviors are very similar large (N≥16) and more variable small datasets, (2) estimator, if we consider mean absolute error κ≤1 relative κ≥1.