Let (X, Y) be a bivariate random vector whose distribution function H(x, y) belongs to the class of bivariate extreme‐value distributions. If F1 and F2 are the marginals of X and Y, then H(x, y) = C{F1(x),F2(y)}, where C is a bivariate extreme‐value dependence function. This paper gives the joint distribution of the random variables Z = {log F1(X)}/{log F1(X)F2(Y)} and W = C{F1{(X),F2(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{F1(X),F2(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.

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