rExtDep {ExtremalDep}

Parametric and semi-parametric random generator of extreme events

Description

This function generates random samples of iid observations from extremal dependence models and semi-parametric stochastic generators.

Usage

rExtDep(n, model, par, angular=FALSE, mar=c(1,1,1), num, threshold, 
        exceed.type)

Arguments

n

An integer indictaing the number of observations.

model

A character string with the name of the model. Parametric model include "HR" (Husler-Reiss), "ET" (Extremal-t), "EST" (Extremal Skew-t). Semi-parametric generators include "semi.bvevd" and "semi.bvexceed".

par

A vector representing the parameters of the (parametric or non-parametric) model.

angular

A logical value; TRUE for angular outputs.

mar

A vector or matrix of marginal parameters.

num

An integer indicating the number of observations the componentwise maxima is computed over. Required when model="HR", "ET" or "EST". Set to 5e+5 unless specified.

threshold

A bivariate vector indicating the level of exceedances. Required when model="semi.bvexceed".

exceed.type

A character string taking value "and" or "or" indicating the type of exceednaces. Required when model="semi.bvexceed".

Details

There is no limit of the dimensionality when model="HR", "ET" or "EST" while model="semi.bvevd" and "semi.bvexceed" can only generate bivariate observations. When angular=TRUE and model="semi.bvevd" or "semi.bvexceed" the simulation of pseudo-angles follows Algorithm 1 of Marcon et al. (2017). When model="semi.bvevd" and angular=FALSE, maxima samples are generated according to Algorithm 2 of Marcon et al. (2017). When model="semi.bvexceed" and angular=FALSE, exceedance samples are generated above value specified by threshold, according to Algorithm 3 of Marcon et al. (2017). exceed.type="and" generates samples that exceed both thresholds while exceed.type="or" generates samples exceeding at least one threshold.

When the argument mar is a vector, the marginal distrutions are identical. When a matrix is provided each row corresponds to a set of marginal parameters. No marginal transformation is applied when mar=c(1,1,1).

Value

A matrix with n rows and p>=2 columns. p=2 when model="semi.bvevd" or "semi.bvexceed".

Author(s)

Simone Padoan, [e-mail], https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, [e-mail] https://www.borisberanger.com;

References

Marcon, G., Naveau, P. and Padoan, S.A. (2017) A semi-parametric stochastic generator for bivariate extreme events Stat, 6, 184-201.

See Also

dExtDep, pExtDep, fExtDep, fExtDep.np

Examples

# Example using the trivariate Husler-Reiss
set.seed(1)
data <- rExtDep(n=10, model="HR", par=c(2,3,3))

# Example using the semi-parammetric generator of maxima
set.seed(2)
beta <- c(1.0000000, 0.8714286, 0.7671560, 0.7569398, 
          0.7771908, 0.8031573, 0.8857143, 1.0000000)
data <- rExtDep(n=10, model="semi.bvevd", par=beta, 
                mar=rbind(c(0.2, 1.5, 0.6),c(-0.5, 0.4, 0.9)))

# Example using the semi-parammetric generator of maxima
set.seed(3)
data <- rExtDep(n=10, model="semi.bvexceed", par=beta, 
                threshold=c(0.2, 0.4), exceed.type="and")