RTDE {RTDE}

Data object used for a Tail Dependence model

Description

Data object used for a Tail Dependence model.

Usage

RTDE(obs=NULL, simu=list(), contamin=list(),
    nbpoint, alpha, omega, method="MDPDE", fix.arg=list(rho=-1),
    boundary.method="log", core=1, keepdata, control=list())


## S3 method for class 'RTDE'
print(x, ...)
## S3 method for class 'RTDE'
summary(object, ...)
## S3 method for class 'RTDE'
plot(x, which=1:3, FUN=mean, main, ...)

prob(object, q, ...)
## Default S3 method:
prob(object, q, ...)
## S3 method for class 'RTDE'
prob(object, q, ...)

Arguments

obs

bivariate numeric dataset.

simu

a names list with components: "nb", "marg", "cop", "replicate". When needed, "cop.par" must be provided, see dataRTDE.

contamin

a names list with components: "eps", "method", "marg", "cop". When needed, "cop.par" must be provided, see dataRTDE.

nbpoint

a numeric for the number of largest points to be selected.

alpha

a numeric for the power divergence parameter.

omega

a numeric for omega, see section Details.

method

a character string equals to "MDPDE".

fix.arg

a named list of fixed arguments: either rho only e.g. list(rho=-1) or rho, delta e.g. list(rho=-1, delta=0).

boundary.method

a character string: either "log" or "simple", see section Details.

core

a numeric for the number of core to be used, only relevant for simulated data.

keepdata

a logical whether to return or not the dataset.

control

A list of control paremeters for fitRTDE.

x, object

an R object inheriting from "RTDE".

...

arguments to be passed to subsequent methods.

which

an integer to specify what to plot: 1 eta, 2 delta, 3 probability estimates.

FUN

the function to be applied, default to mean.

main

a main title for the plot.

q

vector of quantiles.

Details

The function RTDE handles (empirical or simulated) data (cf. dataRTDE) and then fits a bivariate tail model using a method criterion (cf. fitRTDE and MDPD) based on an extended Pareto distribution approximation (EPD). Typical distributions for simulated data and/or contaminations are

• MarginalUnit Pareto upareto, Frechet Frechet.

• CopulaFrank Frank, FGM FGM.

For a good introduction, please refer to references.

Value

RTDE returns an object of class "RTDE" having the following components:

obs.type

see dataRTDE.

data

see dataRTDE.

fit

see fitRTDE.

simu

see dataRTDE.

contamin

see dataRTDE.

setting

a list summarizing the computation.

Author(s)

Christophe Dutang

References

C. Dutang, Y. Goegebeur, A. Guillou (2014), Robust and bias-corrected estimation of the coefficient of tail dependence, Volume 57, Insurance: Mathematics and Economics

This work was supported by a research grant (VKR023480) from VILLUM FONDEN and an international project for scientific cooperation (PICS-6416).

See Also

See fitRTDE for the fitting process and dataRTDE for the data-handling process.

Examples

#####
# (1) simulation

n <- 100
x <- RTDE(simu=list(nb=n, marg="ufrechet", cop="indep", replicate=1),
	nbpoint=10:11, alpha=0, omega=1/2)
x	
summary(x)