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.