Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles

Let ( X, Y ) be a bivariate random vector whose distribution function H(x, y) belongs to the class of bivariate extreme‐value distributions. If F 1 and F 2 are the marginals of X and Y , then H(x, y) = C { F 1 (x), F 2 ( y )}, where C is a bivariate extreme‐value dependence function. This paper gives the joint distribution of the random variables Z = {log F 1 ( X )}/{log F 1 ( X ) F 2 ( Y )} and W = C { F 1 {( X ), F 2 ( Y )}. Using this distribution, an algorithm to generate random variables having bivariate extreme‐value distribution is présentés. Furthermore, it is shown that for any bivariate extreme‐value dependence function C , the distribution of the random variable W = C { F 1 ( X ), F 2 ( Y )} belongs to a monoparametric family of distributions. This property is used to derive goodness‐of‐fit statistics to determine whether a copula belongs to an extreme‐value family.