Extreme-value copulas associated with the expected scaled maximum of independent random variables (Q1749979)

Consider a \(d\)-dimensional extreme-value copula \(C\). It is known that, if \( X_{1},\ldots,X_{d} \) are arbitrary non-negative random variables with unit mean, then the stable tail dependence function \(l\) associated with \(C\) is given by \[ l\left(t_{1},\ldots,t_{d} \right) = \mathrm{E}\left\{ \max \left( t_{1}X_{1},\ldots,t_{d}X_{d} \right) \right\} \] for \( t_{1},\ldots,t_{d} \in \left[0,\infty \right) \). In the special case, when the random variables \( X_{1},\ldots,X_{d} \) are independent and identically distributed, the author detailly studies the de Finetti structure of \(C\).