Correlation Analysis Of Multivariate Directional Variables

This paper studies the measurement of the correlation of multivariate directional data.Directional data are widely used in biology,medicine,geology,astronomy,meteorology and other fields.The research question has certain theory significance and the practical value.This paper focuses on the problem of sample correlation coefficients of multivariate directional variables,mainly based on the form of the sample correlation coefficients of two variables,and the correlation coefficients of several variables are obtained by the relation of the normalized random variables.According to the relation of correlation coefficient and inner product matrix,the quantitative estimation of correlation coefficients is given by the determinant of the inner product matrix,and the properties of the correlation coefficients of multivariate samples are given by analyzing the properties of the inner product matrix.Improve the multivariate correlation metric of directional data.For two related directional variables,the connection function is given by using non trigonometric functions.According to the properties of the connection function,the correlation structure of two directional variables is measured by the distribution,and the concrete manifestation of the correlation of variables in the joint distribution is clearly indicated.It also shows that nonnegative trigonometric sums are more practical in the application of directional data.In order to verify and test the correlation of multivariate directional data.The wind direction data of buoys were obtained from the International Buoy Center website,and the wind direction and rainfall data were obtained from the Northern Spanish Observatory.The sample digital features were computed by R language,the uniformity was tested,the distribution form was displayed and the correlation coefficients were calculated.The properties of the correlation coefficients of the multivariate directional variables are also verified.For the variables with obvious relativity,the correlation of variables can be well reflected by using the nonnegative trigonometric sums copula.And the fitting effect of the joint distribution is very good,which has practical significance.