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9.1. Les différentes mesures de dépendances extrêmes 285
ρ + v=∞ ρ s v=∞ ρu=∞ λ ¯ λ
Bivariate Gaussian 0 1 0 0 ρ
Bivariate Student’s see Table 3 see Table 3 - 2 · ¯ Tν+1
√ν + 1
1−ρ
1+ρ
Gaussian Factor Model 0 1 0 0 ρ
Student’s Factor Model 1 1 -
ρ ν
ρ ν +(1−ρ 2 ) ν/2
Table 4: Asymptotic values of ρ + v , ρs v and ρu for v → +∞ and u → ∞ and comparison with the taildependence
λ and ¯ λ for the four models indicated in the first column. The factor model is defined by (8),
i.e., X = αY + ɛ. ρ is the unconditional correlation coefficient. For the Student’s factor model, Y and ɛ
have centered Student’s distributions with the same number ν of degrees of freedom and their scale factors
are respectively equal to 1 and σ, so that ρ = (1 + σ2
α2 ) −1/2 . For the Bivariate Student’s distribution, we
refer to Table 1 for the constant values of ρ + v=∞ and ρs v=∞.
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