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If the interest is to calibrate two instruments then the functional relationship model is more appropriate than regression models. Fitting a straight line when both variables are circular and subject to errors has not received much attention. In this paper, we consider the problem of detecting influential points in two functional relationship models for circular variables. The first is based on the simple circular regression the (SC), while the last is derived from the complex linear regression the (CL).


The covariance matrices are derived and then the COVRATIO statistics are formulated for both models. The cut-off points are obtained and the power of performance is assessed via simulation studies.


The performance of COVRATIO statistics depends on the concentration of error, sample size and level of contamination. In the case of linear relationship between two circular variables COVRATIO statistics of the (SC) model performs better than the (CL).

 On the other hand, a novel diagram, the so-called spoke plot, is utilized to detect possible influential points

For illustration purposes, the proposed procedures are applied on real data of wind directions measured by two different instruments. COVRATIO statistics and the spoke plot were able to identify two observations as influential points.


Correlation radar errors estimation wind.

Article Details

Author Biography

ALi Hassan Abuzaid, Department of Mathematics, Faculty of Science, Al-Azhar University-Gaza, Gaza, Palestine

Assiatant Professor of Statistics,

Department of Mathematics,

Faculty of Science, Al-Azhar University-Gaza,
Gaza, Palestine

How to Cite
Abuzaid, A. H. (2013). ON THE INFLUENTIAL POINTS IN THE FUNCTIONAL CIRCULAR RELATIONSHIP MODELS WITH AN APPLICATION ON WIND DATA. Pakistan Journal of Statistics and Operation Research, 9(3), 333-342.

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