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.
Highlights
Adcock (1877, 1878) explored Errors-in-variables model (EIVM) as a practical statistical approach for modelling different problem (Gillard, 2010)
The main difference between ordinary regression and EIVM is that the response and explanatory variables in EIVM have no distinction; both are measured with errors, unlike in the regression model, where only the response variable is measured with errors
Ibrahim (2013) and Satari et al (2014) developed new versions of the functional relationship model on the basis of Sarma and Jammalamadaka's (1993) and Downs and Mardia's (2002) circular-circular regression models, respectively. All of these previous models assumed that errors follow von Mises distribution with mean 0 and a constant concentration parameter, while Abuzaid et al (2018) proposed a simple functional relationship model based on Abuzaid and Allahham's (2015) circular regression model by assuming that errors follow the wrapped Cauchy distribution
Summary
Adcock (1877, 1878) explored Errors-in-variables model (EIVM) as a practical statistical approach for modelling different problem (Gillard, 2010). Ibrahim (2013) and Satari et al (2014) developed new versions of the functional relationship model on the basis of Sarma and Jammalamadaka's (1993) and Downs and Mardia's (2002) circular-circular regression models, respectively All of these previous models assumed that errors follow von Mises distribution with mean 0 and a constant concentration parameter, while Abuzaid et al (2018) proposed a simple functional relationship model based on Abuzaid and Allahham's (2015) circular regression model by assuming that errors follow the wrapped Cauchy distribution. This paper proposes a new version of the functional relationship model by assuming that errors are originated from hybrid distributions, for instance von Mises and wrapped Cauchy distributions. This section proposes a new version of the circular functional relationship models by assuming that the errors are originated from von Mises and wrapped Cauchy distributions with known ratio of error concentrations,
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