Pickands dependence function for the Extremal Skew-$t$ model.

Description

Evaluate the bivariate and trivariate Pickands dependence function for the bivariate skew-normal.

Usage

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	pk.extst(x, param)

Arguments

x

a vector of length 2 or 3 that belongs to the corresponding simplex.

param

the parameter vector, containing the dependence, shape and df parameters.

Details

In the bivariate case, there is 1 dependence parameter, 2 shape parameters and a degree of freedom. In the trivariate case, there is 3 dependence parameter, 3 shape parameters and a degree of freedom. Dependence parameters must be between -1 and 1, the degree of freedom must be positive.

Author(s)

Simone Padoan, simone.padoan@unibocconi.it, faculty.bocconi.it/simonepadoan; Boris Beranger, borisberanger@gmail.com

References

Padoan, S. A. (2011). Multivariate extreme models based on underlying skew-t and skew-normal distributions. Journal of Multivariate Analysis, 102, 977-991.

Examples

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### Upper tail dependence

pk.extst(x=c(0.5,0.5), param=c(0.4,-2,4,3))

### Lower tail dependence

pk.extst(x=c(0.2,0.4,0.4), param=c(0.4,0.3,0.7,3,-1,0,2))

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