On tail dependence for Grubbs' copula-function

We consider Grubbs' statistics for a normal sample. Those statistics are the standardized maximum and standardized minimum. We investigate the distribution properties of Grubbs' statistics and construct a new copula-function by an inversion method from the joint distribution of Grubbs' statistics. We also describe properties of the constructed Grubbs' copula-function. It is proved that this copula is symmetric. We give examples of plots of the simulated values from Grubbs' copula. It is found that Grubbs' copula-function allows to describe negative dependencies between random variables. It is proved that for Grubbs' copula-function coefficients of the upper-left and lower-right tail dependencies are equal each other. We find the formula for calculation of these coefficients and execute model calculations of tail dependencies coefficients for Grubbs' copula.