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Circular Functional Relationship Model with Wrapped Cauchy Errors

Author(s)
Ali H. Abuzaid Department of Mathematics, Faculty of Science, Al Azhar University – Gaza, Palestine
Walaa A. Abu El-laban Department of Applied Statistics, Faculty of Economic and Administrative Sciences Al Azhar University – Gaza, Palestine
Abdul Ghapor Hussin Department of Defence Science, Faculty of Defence Science and Technology National Defence University of Malaysia, Malaysia
Abstract
This paper extends the simple linear regression model with wrapped Cauchy error to the functional case when both variables are subjected to wrapped Cauchy errors. Assuming the ratio between the two error variances is known and the slope parameter equals one the maximum likelihood estimates are obtained. The closed-form expression for the maximum likelihood estimators are not available and the estimates are obtained iteratively by choosing a suitable initial values. The quality of estimates and the accuracy of the model are illustrated via simulations and the results revealed an acceptable performance of the estimators where they are unbiased, consistent and robust. The sampling variances of the model parameters are obtained via bootstrapping methods and consequently the confidence intervals were constructed. The proposed model is illustrated with an application on the analysis of wind directions data at two cities in the Gaza strip, Palestine.
Publication Details
Page(s) 275-287
DOI DOI not available
Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 14, Issue: 2, Year: 2018

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Keywords
Bootstrap, Robustness, EIVM, Wind direction
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