Efficient Approximation for the von Mises Concentration Parameter

This study discusses some of the approximation which can be used to obtain the maximum likelihood estimate of the concentration parameter of the von Mises distribution. This study shows that the efficient approximation may also be obtained by solving the equation for the ratio of the modified Bessel function of first kind of order one and first kind of order zero. The closed-form solution for parameter concentration is also given. We have found out that the new proposed method performs well especially for large κ.