بناء و تقدير أنموذج انحدار زاوي للبيانات الدائري مع تطبيق

Constructing and Estimating an Angular Regression Model for Circular Data with Practical Application

The study of variables with circular data is one of the important processes in our present time due to the presence of some phenomena that are described by this type of data, and the angular regression (circular) is one of the most important statistical methods to represent this type of phenomena, and the method of maximum likelihood estimation (MLE) is described as one of the most important methods that are used to estimate its parameters. The random error distribution of the angular regression model is also important because the method of MLE depends mainly on maximizing the probability density function of the random error distribution.
Therefore, the study included the use of three (circular) angular regression models, namely, the angular regression model with von Mises error, the simple angular regression model with an error that follows the wrapped Cauchy distribution, and the proposed model, which is the simple angular regression model with an error that follows the wrapped normal distribution.
A test of the quality of reconciliation of the three models was proposed based on the Fisher distribution to indicate the significance of each of the three models. A comparison was made between the three models using two criteria: the Bayesian Information Criterion (BIC) and the Akaikes Debugger Information Criterion (AICC).
And the results showed on the experimental side that all that was matched between the distribution of the dependent variable with the distribution of random error, the model is the best model, according to what was shown by the value of the standard (BIC) and the standard ((AICC), and between the quality of reconciliation test for the models that most of the models are moral models. The practical application was done on two circular variables, namely the wind direction in the city of Nasiriyah as a dependent variable and the direction of high atmospheric pressure as an independent variable. The results showed that all models represented the data correctly by passing the estimated models to test the quality of reconciliation, and that the relationship between the direction of high atmospheric pressure and the direction of the winds in the city of Nasiriyah is a direct relationship. The proposed model, which is the simple angular regression model with an error that follows the wrapped normal distribution, is the optimal model for this data, as indicated by the value of (BIC) and (AICC) criterion.