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A few words on copula
Express a multivariate cumulative distribution function as
a function of its univariate marginal distributions
Π 𝑢1, 𝑢2 = ℙ 𝑈1 ≤ 𝑢1, 𝑈2 ≤ 𝑢2 = C(F 𝑢1 , G 𝑢2 )
Many types of copulas
Parametric : archimedean (e.g. : C 𝑢, 𝑣 = 𝑢𝑣) , gaussian
Non parametric : empirical
Development of a new copula : Indetermination criteria
𝐶 𝑢1, 𝑢2 = 𝑢2
𝐹−1(𝑢1)
𝐴
+ 𝑢1
𝐺−1(𝑢2)
𝐵
-
𝐹−1(𝑢1)𝐺−1(𝑢2)
𝐴𝐵