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

Abstract

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 μ, several methods have been proposed to estimate the concentration parameter κ. We here provide a thorough evaluation of the behavior of 12 such estimators for datasets of size N ranging from 2 to 8192 generated with a κ ranging from 0 to 100. We provide detailed results as well as a global analysis of the results, showing that (1) for a given κ, most estimators have behaviors that are very similar for large datasets ($N\ge 16$) and more variable for small datasets, and (2) for a given estimator, results are very similar if we consider the mean absolute error for $\kappa \le 1$ and the mean relative absolute error for $\kappa \ge 1.$

Keywords:

• Circular data
• Comparison
• Concentration parameter
• Estimation
• Von Mises distribution