Parameter Estimation for Circular Simultaneous Functional Relationship Model (CSFRM) for Unequal Variances

Abstract

In this study, we propose an extended model of the Circular Simultaneous Functional Relationship Model from the Circular Functional Relationship Model. In this case, the circular model and the circular variable will be applied assuming the error variances are not equal. All estimations of the parameter followed von Mises distribution. The angular and slope parameters are obtained using the ms function, while concentration parameter estimation is obtained from the polyroot function provided in the SPLUS statistical package. The simulation study has been conducted to assess the efficiency of the proposed model. The simulation results showed that as sample size and concentration parameters increase, all parameters’ estimates are close to the true value and have a smaller bias. The illustration of real wind and wave direction data from two different bases of data is given to show its practical applicability. We note that the proposed method for parameter estimation works well with the proposed model in the case of unequal error variances as it provides good estimates.

Keywords: circular simultaneous functional relationship model, ms function, parameter estimates, polyroot function, unequal variances