stdf {ReIns} | R Documentation |
Non-parametric estimators of the STDF
Description
Non-parametric estimators of the stable tail dependence function (STDF): and
.
Usage
stdf(x, k, X, alpha = 0.5)
stdf2(x, k, X)
Arguments
x |
A |
k |
Value of the tail index |
X |
A data matrix of dimensions |
alpha |
The parameter |
Details
The stable tail dependence function in can be estimated by
with
where is the rank of
among the
observations in the
-th dimension:
This estimator is implemented in stdf
.
The second estimator is given by
where is the
-th smallest observation in the
-th dimension.
This estimator is implemented in
stdf2
.
See Section 4.5 of Beirlant et al. (2016) for more details.
Value
stdf
returns the estimate and
stdf2
returns the estimate .
Author(s)
Tom Reynkens
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.
Examples
# Generate data matrix
X <- cbind(rpareto(100,2), rpareto(100,3))
# Tail index
k <- 20
# Point to evaluate the STDF in
x <- c(2,3)
# First estimate
stdf(x, k, X)
# Second estimate
stdf2(x, k, X)