Function tailInt

Description

Integral of the bivariate parametric stable tail dependence function over the unit square, for the Smith model or the Brown-Resnick process.

Usage

1
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 = (α, ρ, β, c).

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 < α < 1, ρ > 0, 0 < β ≤ π/2 and c > 0.

Value

A scalar.

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.

See Also

Mestimator, tailIntEmp

Examples

1
2
tailInt(loc = cbind(c(1,1),c(2,3)), model = "smith", theta = rbind(c(3,1),c(1,2)))
tailInt(loc = cbind(c(1,2),c(3,4)), model = "BR", theta = c(1.5,1,0.5,0.75))