Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance

Abstract

In this study, we propose the estimation of the concentration parameter for simultaneous circular functional relationship model. In this case, the variances of the error term are not necessarily equal and the ratio of the concentration parameter λ = is not necessarily 1. The modified Bessel function was expended by using the asymptotic power series and it became a cubic equation of κ. From the cubic equation of κ, the roots were obtained by using the polyroot function in SPlus software. Simulation study was done to study the mean, estimated bias, absolute relative estimated bias, estimated standard error and estimated root mean square error of the estimation of the concentration parameter. From the simulation study, large concentration parameter and sample size show that the estimated concentration parameter has smaller bias. Also, an illustration to a real wind and wave data set is given to show its practical applicability.