Calibration Function of a Bivariate Copula for a Given Parameter's Value

Computes the calibration function (eta) of a bivariate copula for a given value of the (first) copula parameter.

BiCopPar2Eta(family, par)

Arguments

family

A copula family: 1 Gaussian, 2 Student t, 301 Double Clayton type I (standard and rotated 90 degrees), 302 Double Clayton type II (standard and rotated 270 degrees), 303 Double Clayton type III (survival and rotated 90 degrees), 304 Double Clayton type IV (survival and rotated 270 degrees), 401 Double Gumbel type I (standard and rotated 90 degrees), 402 Double Gumbel type II (standard and rotated 270 degrees), 403 Double Gumbel type III (survival and rotated 90 degrees), 404 Double Gumbel type IV (survival and rotated 270 degrees).

par

The (first) copula parameter

Value

The value of the calibration function, depending on the copula parameter and family as:

• 1 Gaussian, f(x) = 2*atanh(x)

• 2 Student t, f(x) = 2*atanh(x)

• 301 Double Clayton type I (standard and rotated 90 degrees), f(x) = x

• 302 Double Clayton type II (standard and rotated 270 degrees), f(x) = x

• 303 Double Clayton type III (survival and rotated 90 degrees), f(x) = x

• 304 Double Clayton type IV (survival and rotated 270 degrees), f(x) = x

• 401 Double Gumbel type I (standard and rotated 90 degrees), f(x) = x*(1-1/abs(x))

• 402 Double Gumbel type II (standard and rotated 270 degrees), f(x) = x*(1-1/abs(x))

• 403 Double Gumbel type III (survival and rotated 90 degrees), f(x) = x*(1-1/abs(x))

• 404 Double Gumbel type IV (survival and rotated 270 degrees) f(x) = x*(1-1/abs(x)).

See also

BiCopEta2Par or BiCopPar2Tau and BiCopTau2Par from VineCopula.