Several Correlation Measurements Of Circular Data

The correlation analysis of circular data is a new field of statistics.Firstly,according to the population correlation coefficient of the two circular variables,combined with the idea of product correlation coefficient and standardized vectors in the linear correlation analysis,this paper gives the sample correlation coefficient of the two circular variables,and the correlation coefficient of the three circular variables is defined by extending the two variables to three variables.On this basis,the range,the maximum value and minimum value of the correlation coefficients of two or three circular variables are discussed by using the circular standard vector,as the same as the necessary and sufficient conditions are established.Secondly,in the correlation analysis of multiple variables,there is a mutual influence between the variables.Only the product correlation coefficient between the two variables cannot be used to reflect the internal correlation between the variables.In order to eliminate the interaction between the variables,we need to use the first-order partial correlation coefficient and the T test statistics to analyze the degree of partial correlation and significance level between variables.It accurately leads to reflect the internal correlation between the two variables.Furthermore,in the statistics,the correlation coefficient is the measure of the statistical differences between the individual categories or the gap between the whole group and the single sample.The definition of the circular correlation ratio is given,and the category dispersion or the overall dispersion of the circular variables can be analyzed by the correlation ratio.In order to examine the rationality and maneuverability of the theories,this paper obtains the observations data of the Global Ship Station and the China Meteorological Station.Based on the real observations of circular data in the data set,R language software for product correlation,partial correlation,rank correlation and correlation ratio is used in the simulation experiments.Comparing the applicable conditions and characteristics of different correlation analysis methods,this paper summarizes the rules of the correlation analysis of circular data.