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Abstract

The modeling of functional relationship between circular variables is gaining an increasing interest. Existing models assume the errors have same distributions, but the case of different distributional errors is yet as 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. Results show a direct relationship between the performance of parameters estimates and the sample size, and the concentration parameters.
For illustration, the proposed models are applied on wind directions data in two main cities in the Gaza Strip, Palestine.