A statistical method to describe the relationship of circular variables simultaneously

This paper proposes a statistical model to compare or describe the relationship between several circular variables which are subjected to measurement errors. The model is known as the simultaneous linear functional relationship for circular variables and it is, in fact, an extension of the linear functional relationship model. Maximum likelihood estimation of parameters has been obtained iteratively by assuming that the ratios of concentration parameters are known and by choosing suitable initial values. In particular, an improved estimate of the concentration parameter is proposed. In addition, the variance and covariance of parameters have been derived using the Fisher information matrix. To illustrate the applicability of the model to real data, the relationship of the Malaysian wind direction data recorded at various levels is described