Description Usage Arguments Details Value References Examples
An Implementation of the procedure proposed in Drees & Kaufmann (1998) for selecting the optimal sample fraction in tail index estimation.
1 |
data |
vector of sample data |
r |
tuning parameter for the stopping criterion. |
The procedure proposed in Drees & Kaufmann (1998) is based on bias reduction. A stopping criterion with respect to k
is implemented to find the optimal tail fraction, i.e. k/n
with k
the optimal number of upper order statistics. This number, denoted k0
here, is equivalent to the number of extreme values or, if you wish, the number of exceedances in the context of a POT-model like the generalized Pareto distribution. k0
can then be associated with the unknown threshold u
of the GPD by choosing u
as the n-k0
th upper order statistic. If the above mentioned stopping criterion exceedes a certain value r
, the bias of the assumed extreme model has become prominent and therefore k
should not be chosen higher. For more information see references.
second.order.par |
gives an estimation of the second order parameter |
k0 |
optimal number of upper order statistics, i.e. number of exceedances or data in the tail |
threshold |
the corresponding threshold |
tail.index |
the corresponding tail |
Drees, H. and Kaufmann, E. (1998). Selecting the optimal sample fraction in univariate extreme value estimation. Stochastic Processes and their Applications, 75(2), 149–172.
1 2 |
Loading required package: eva
$sec.order.par
[1] -4.844346
$k0
[1] 64
$threshold
[1] 14.39458
$tail.index
[1] 1.730787
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.