CORRELATION FUNCTION AND DEPENDENCE FUNCTION FOR MULTIVARIATE EXTREMES OF RAINFALL

Abstract

 Extremes of rainfall at several sites are important elements to examine the total amount of precipitation for the drainage basin, and the correlation should be taken into consideration to evaluate the flood risk. Dependence function has been investigated in the context of theoretical statistics for multivariate extremes, because such item can be only defined for the excess over either threshold of the components. However it gives the indirect properties of the component-wise maxima which have occurred in the same year and which were not caused by the same rainfall. Here a newly defined correlation function is proposed in this paper by employing the occurrence numbers which includes the joint exceedance of all components and the partial exceedance of at least one component. Numerical simulations are also implemented and demonstrated to show the statistical variabilities.