Integral of the bivariate parametric stable tail dependence function over the unit square, for the Smith model or the Brown-Resnick process.
Usage
tailInt(loc, model, theta)
Arguments
loc
A 2 x 2 matrix, where a row represents a location.
model
Choose between "smith" and "BR".
theta
Parameter vector. For the Smith model, theta must be equal to the 2 x 2 covariance matrix. For the Brown-Resnick pocess, theta $ = (\alpha, \rho, \beta, c)$.
Value
A scalar.
Details
This is an analytic implementation of the integral of the stable tail dependence function,
which is much faster than numerical integration. For the definitions of the parametric stable tail dependence
functions, see Einmahl et al. (2014).
The parameter vector theta must be a positive semi-definite matrix if model = "smith"
and a vector of length four if model = "BR", where $0 < \alpha < 1$, $\rho > 0$,
$0 < \beta \le \pi/2$ and $c > 0$.
References
Einmahl, J.H.J., Kiriliouk, A., Krajina, A. and Segers, J. (2014), "An M-estimator of spatial tail dependence". See http://arxiv.org/abs/1403.1975.