Description Usage Arguments Details Value References Examples
An Implementation of the procedure proposed in Danielsson et al. (2016) for selecting the optimal threshold in extreme value analysis.
1 |
data |
vector of sample data |
ts |
size of the upper tail the procedure is applied to. Default is 15 percent of the data |
method |
should be one of |
The procedure proposed in Danielsson et al. (2016) minimizes the distance between the largest upper order statistics of the dataset, i.e. the empirical tail, and the theoretical tail of a Pareto distribution. The parameter of this distribution are estimated using Hill's estimator. Therefor one needs the optimal number of upper order statistics k
. The distance is then minimized with respect to this k
. The optimal 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 saying u
is the n-k0
th upper order statistic. For the distance metric in use one could choose the mean absolute deviation called mad
here, or the maximum absolute deviation, also known as the "Kolmogorov-Smirnov" distance metric (ks
). For more information see references.
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 index by plugging in |
Danielsson, J. and Ergun, L.M. and de Haan, L. and de Vries, C.G. (2016). Tail Index Estimation: Quantile Driven Threshold Selection.
1 2 |
Loading required package: eva
$k0
[1] 17
$threshold
[1] 29.02604
$tail.index
[1] 1.625417
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