HRcop: The Hüsler-Reiss Extreme Value Copula

In wasquith/copBasic: General Bivariate Copula Theory and Many Utility Functions

The Hüsler–Reiss Extreme Value Copula

Description

The Hüsler–Reiss copula (Joe, 2014, p. 176) is

\mathbf{C}_{\Theta}(u,v) = \mathbf{HR}(u,v) = \mathrm{exp}\bigr[-x \Phi(X) - y\Phi(Y)\bigr]\mbox{,}

where \Theta \ge 0, x = - \log(u), y = - \log(v), \Phi(.) is the cumulative distribution function of the standard normal distribution, X and Y are defined as:

X = \frac{1}{\Theta} + \frac{\Theta}{2} \log\biggl(\frac{x}{y}\biggr)\mbox{\ and\ } Y = \frac{1}{\Theta} + \frac{\Theta}{2} \log\biggl(\frac{y}{x}\biggr)\mbox{.}

As \Theta \rightarrow 0^{+}, the copula limits to independence (\mathbf{\Pi}; P). The copula here is a bivariate extreme value copula (BEV), and the parameter \Theta requires numerical methods.

Usage

HRcop(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 \Theta 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

P, GHcop, GLcop, tEVcop

Examples

# Parameter Theta = pi recovery through the Blomqvist Beta (Joe, 2014, p. 176)
qnorm(1 - log( 1 + blomCOP(cop=HRcop, para=pi) ) / ( 2 * log(2) ) )^(-1)

wasquith/copBasic documentation built on Feb. 17, 2025, 11:39 a.m.