ExtremalDep (version 0.0.3-5)

exponent_extr_mod: Exponent function of extremal dependence models

Description

Evaluates the bivariate or trivariate exponent function of the Husler-Reiss, Extremal-$t$ and Extremal Skew-$t$ models.

Usage

exponent_extr_mod(model, z, param, dist)

Value

Returns a single value corresponding to the exponent function or value of the distribution.

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.

dist

Logical; if TRUE the distribution of the model is returned.

Author

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

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.

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()){
exponent_extr_mod(model="hr", z=c(2,3), param=1.2, dist=FALSE)
exponent_extr_mod(model="hr", z=c(2,3,1), param=c(1.2,1,1.4), dist=TRUE)
}

### Extremal-t

if (interactive()){
exponent_extr_mod(model="Extremalt", z=c(0.1,2), param=c(0.5,2), dist=FALSE)
exponent_extr_mod(model="Extremalt", z=c(0.1,2,3), param=c(0.5,0.4,0.9,2), dist=TRUE)
}

### Extremal Skew-t

if (interactive()){
exponent_extr_mod(model="Skewt", z=c(0.1,2), param=c(0.5,0,0,2), dist=FALSE)
exponent_extr_mod(model="Skewt", z=c(0.1,2,3), param=c(0.5,0.4,0.9,0,0,0,2), dist=TRUE)
exponent_extr_mod(model="Skewt", z=c(0.1,2,3), param=c(0.5,0.4,0.9,1,10,-5,2), dist=TRUE)
}