Approximation of error concentration parameter for simultaneous circular functional model

In this study, we propose a simple procedure for obtaining estimate of the concentration parameter of the von Mises distribution for the simultaneous circular functional relationship model. Currently, the concentration parameter for this model can only be estimate by assuming the ratio of the error concentration parameter λj is equal to one. This new proposed method can be applied for any value of λ based on the expansion of the asymptotic power series of the modified Bessel function. Finally, the simulation study has been carried out to verify the accuracy of the new proposed procedure.