excess_pr_extr_mod {ExtremalDep}

R Documentation

Exceedance Probability for extremal dependence models

Description

Exceedance Probability for bivariate or trivariate Husler-Reiss, Extremal-$t$ and Extremal Skew-$t$ models.

Usage

	excess_pr_extr_mod(model, z, param)

Arguments

model	A string with the name of the model: "hr", "Extremalt" or "Skewt".
z	A vector of length 2 or 3, containing strictly positive reals.
param	A vector containing the parameters of the model. See Details.

Details

If model="hr" then the parameter vector is made of choose(d,2) positive parameters, d=2,3. If model="Extremalt" then the parameter vector is made of choose(d,2) dependence parameters and a degree of freedom, d=2,3. If model="Skewt" then the parameter vector is made of choose(d,2) dependence parameters, d shape (or skewness) parameters and a degree of freedom, d=2,3.

Value

Returns a probability.

Author(s)

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

References

Beranger, B. and Padoan, S. A. (2015). Extreme dependence models, chapater of the book Extreme Value Modeling and Risk Analysis: Methods and Applications, Chapman Hall/CRC.

Beranger, B., Padoan, S. A. and Sisson, S. A. (2017). Models for extremal dependence derived from skew-symmetric families. Scandinavian Journal of Statistics, 44(1), 21-45.

Examples

### Husler-Reiss

if (interactive()){
excess_pr_extr_mod(model="hr", z=c(1,3), param=0.5)
excess_pr_extr_mod(model="hr", z=c(1,3,5), param=c(5,4,2))
excess_pr_extr_mod(model="hr", z=c(0.001,0.001,0.001), param=c(5,4,2))
}

### Extremal-t

if (interactive()){
excess_pr_extr_mod(model="Extremalt", z=c(0.1,0.3), param=c(0.5,2))
excess_pr_extr_mod(model="Extremalt", z=c(1,3,5), param=c(0.5,0.4,0.8,2))
excess_pr_extr_mod(model="Extremalt", z=c(0.001,0.001,0.001), param=c(0.5,0.4,0.8,2))
}

### Extremal Skew-t

if (interactive()){
excess_pr_extr_mod(model="Skewt", z=c(0.1,0.3), param=c(0.5,0,0,2))
excess_pr_extr_mod(model="Skewt", z=c(0.1,0.3), param=c(0.5,-10,-4,2))
excess_pr_extr_mod(model="Skewt", z=c(1,3,5), param=c(0.5,0.4,0.8,0,0,0,2))
excess_pr_extr_mod(model="Skewt", z=c(1,3,5), param=c(0.5,0.4,0.8,1,5,10,2))
excess_pr_extr_mod(model="Skewt", z=c(0.001,0.001,0.001), param=c(0.5,0.4,0.8,1,5,10,2))
}

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