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In particular, this is the case when at least two components η$_{s}$ , η$_{t}$ , s ̸ = t , are independent, see the argument in Section 2. 

Example 3.5 (Bernoulli model) . Consider a standard max-stable rv η ∈ R d with corresponding D -norm ‖·‖$_{B}$$_{β}$ , β ∈ (0 , 1], known from Example 2.7. It is easy to see that 

From the general equality 

where ˜ η is some standard max-stable rv with D -norm ‖·‖$_{D}$ , we conclude 

For another example, namely the logistic model, we refer to Example 4.4. 

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Remark 3.6 . (i) Theorem 3.1 implies that the extremal concurrence probability, just like the dual D -norm function, does not depend on the choice of Z , but only on ‖·‖$_{D}$ . 

(ii) In the preceding theorem, we can replace U , U $^{(1)}$, U $^{(2)}$, . . . by a sequence of iid stochastic processes X , X $^{(1)}$, X $^{(2)}$, . . . whose univariate marginal df F$_{s}$ ( x ) = P ( X$_{s}$ ≤ x ), s ∈ S , are continuous and strictly monontonically increasing on their support. The conditions (6) and (7) will then have to apply to the copula process ( F$_{s}$ ( X$_{s}$ ))$_{s}$$_{∈}$$_{S}$. In that case, 

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where Z is a generator of the D -norm corresponding to the copula expan- sion of ( F$_{s}$ ( X$_{s}$ ))$_{s}$$_{∈}$$_{S}$. Hence, the probability that there is a champion among X $^{(1)}$, . . . , X ( n ) does not depend on the univariate margins, but rather on the copula process of X . 

