The Galambos Extreme Value Copula

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Description

The Galambos copula (Joe, 2014, p. 174) is

\mathbf{C}_{Θ}(u,v) = \mathbf{GL}(u,v) = uv\,\mathrm{exp}\{[x^{-Θ} + y^{-Θ}]^{-1/Θ}\}\mbox{,}

where Θ \in [0, ∞), x = -\log(u), and y = -\log(v). As Θ \rightarrow 0^{+}, the copula limits to independence (\mathbf{Π}; P) and as Θ \rightarrow ∞, the copula limits to perfect association (\mathbf{M}; M). The copula here is a bivariate extreme value copula (BEV), and the parameter Θ requires numerical methods.

Usage

1
GLcop(u, v, para=NULL, ...)

Arguments

u

Nonexceedance probability u in the X direction;

v

Nonexceedance probability v in the Y direction;

para

A vector (single element) of parameters—the Θ parameter of the copula; and

...

Additional arguments to pass.

Value

Value(s) for the copula are returned.

Author(s)

W.H. Asquith

References

Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.

See Also

M, P, GHcop, HRcop, rhobevCOP

Examples

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# Parameter Theta = pi recovery through Blomqvist Beta (Joe, 2014, p. 175)
log(2)/(log(log(2)/log(1+blomCOP(cop=GLcop, para=pi))))

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