GENERAL UNREPLICATED LINEAR FUNCTIONAL RELATIONSHIP MODEL FOR CIRCULAR VARIABLES WITH WIND DIRECTION APPLICATION

Abstract

The functional relationship model is typically used to describe the nature of data that contains unobservable errors.  The general unreplicated linear functional relationship model is discussed in this paper, which can be used to examine circular data with measurement errors.  All factors involved in the unreplicated linear functional relationship model, such as the rotation parameter, slope parameter, and concentration parameter for both observed variables, where the ratio is known and can be equal or unequal, will be evaluated.  This model's parameter estimation is somewhat difficult, however, it is possible to achieve numerical results using a simple iteration technique.  To validate, analyze, and investigate the model's performance, a simulation study was constructed utilizing Monte Carlo simulation.  The results reveal that, in general, estimation bias is minimal and acceptable. The concept is demonstrated using an application to the analysis of a real-world wind direction data collection.