Different Distributional Errors-In-Circular-Variables Models

The modeling of functional relationship between circular variables is gaining an increasing interest. The existing models assume the errors have same probability distributions, but the case of different distributional errors is not yet investigated. This paper considers the modeling of functional relationship for circular variables with different distributional errors. Two functional relationship models are proposed by assuming a combination of von Mises and wrapped Cauchy errors, with a distinction between known and unknown ratio of error concentrations. Parameters of the proposed models are estimated using the maximum likelihood method based on numerical iterative procedures. The properties of parameters' estimators are investigated via an extensive simulation study. The results show a direct relationship between the performance of parameters' estimates and the sample size, as well as the concentration parameters. For illustration, the proposed models are applied on wind directions data in two main cities in the Gaza Strip, Palestine.