ExtremalDep (version 0.0.3-5)

chi.bsn: Tail dependence coefficient for the skew-normal distirbution

Description

Evaluates the upper and lower tail dependence coefficients for the bivariate skew-normal.

Usage

chi.bsn(u, corr=0, shape=rep(0,2), tail="upper")

Value

Returns a value that is strictly greater than \(0\) and less than \(1\)

for the upper coefficient, and between \(-1\) and \(1\) for the lower coefficient.

Arguments

u

a real value in \([0,1]\).

corr

the correlation parameter, between \(-1\) and \(1\).

shape

a numeric vector of real values of length \(2\) with the skewness parameters.

tail

the string "upper" or "lower".

Author

Simone Padoan, , https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, https://www.borisberanger.com/;

Details

Approximation, the tail dependence is obtained in the limiting case where uu goes to eqn11.

References

Bortot, P. Tail dependence in bivariate skew-normal and skew-t distributions. Unpublished.

Examples

### Upper tail dependence

if (interactive()){
chi.bsn(u=0.9,corr=0.5, shape=c(1,-2), tail="upper")
}

### Lower tail dependence

if (interactive()){
chi.bsn(u=0.9, corr=0.5, shape=c(1,-2), tail="lower")
}