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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.
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Abuzaid, A. and Allahham, N. (2015).Simple circular model assuming wrapped Cauchy error. Pakistan Journal of Statistics, 31 (4), 385-398.
Abuzaid, A. H. (2010). Some Problems for Outliers Circular Data. Ph.D. Thesis, University of Malaya, Kuala Lumpur, Malaysia.
Abuzaid, A.H., Abuallaban, W.A. and Hussin, A.G. (2018). Circular Functional Relationship Model with Wrapped Cauchy Errors, Pakistan Journal of Statistics and Operation Research, 14 (2), 287-299.
Adcock, R. J. (1877). Note on the method of least squares, Analyst, 4, 183-184.
Adcock, R. J. (1878). A problem in least squares, Analyst, 5 (1), 53-54.
Badawi, A. S. (2013). An Analytical Study for Establishment of Wind Farms in Palestine to Reach the Optimum Electrical Energy. Master Thesis. The Islamic University of Gaza, Palestine.
Caires, S. and Wyatt, L. R. (2003). A linear functional relationship model for circular data with an application to the assessment of ocean wave measurements. Journal of Agricultural Biological and Environmental Statistics, 8 (2), 153-169.
Downs, T. D. and Mardia, K. V. (2002). Circular regression. Biometrika, 89 (3), 683-697.
Gillard, J. (2010). An overview of linear structural models in errors in variables regression, REVSTAT – Statistical Journal, 8 (1), 57-80.
Hussin, A.G. (1997). Psuedo-Replication in functional relationship with environmental application. Ph.D. Thesis. University of Sheffield, England.
Hussin, A. G., and Chik, Z. (2003). On estimating error concentration parameter for circular functional model. Bulletin of the Malaysian Mathematical Sciences Society, 26(2), 181-188.
Hussin, A.G. (2005). Approximating Fisher’s information for the replicated linear circular functional relationship model. Bull. Malays. Math. Sci. Soc., 28(2), 1-9.
Ibrahim, S. (2013). Some Outlier Problems in a Circular Regression Model. Ph.D. Thesis, University of Malaya, Kuala Lumpur, Malaysia.
Jammalamadaka, S. R. and Sarma, Y. R. (1993). Circular regression. In Matusita, K., editor, Statistical Theory and Data Analysis, 109-128. VSP, Utrecht.
Kendall, M.G. (1951). Regression, structure and functional relationship, Part I, Biometrika, 38 (1/2), 11-25.
Kendall, M.G. (1952). Regression, structure and functional relationship, Part II, Biometrika, 39 (1/2), 96-108.
Oldham, K.B., Myland, J. and Spanier, J. (2010). An Atlas of Functions: with equator, the atlas function calculator. Springer, New York.
Satari, S.Z., Hussin, A.G., Zubairi, Y.Z. and Hassan, S.F. (2014). A new functional relationship model for circular variables. Pakistan Journal of Statistics. 30 (3), 397-410.
Zubairi, Y.Z., Hussain, F. and Hussin, A.G. (2008). An Alternative Analysis of Two Circular Variables via Graphical Representation to the Malaysian Wind Data. Computer and information Science, 1(4), 3-8.