Geology Reference
In-Depth Information
Fig. 8.1 Statistical Blockade: a basic steps; b tail definition
works in the tail portion of our distribution to pick the peak values (based on our
threshold) from the MC generated values. In other words, we can say that this
approach is partially similar to the peaks over threshold (POT) method [generalized
Pareto distribution (GPD) to the exceedances over some threshold]. In the POT
method, the used data are from historical records and not synthetically generated,
whereas, in SB,
generated data is used [
5
]. A schematic representation
of SB is given in Fig.
8.1
a, assuming that threshold value
'
synthetically
'
flood time series is at 90 %.
In statistics, Extreme Value Theory (EVT) deals with the extreme deviations from
the median of probability distributions. In other words, EVT is amathematical method
to build the model of the tail part of the distribution. Assuming that t is the threshold of
the cumulative distribution (CDF), F(x) means that the tail part of the distribution
consists of the values above t. The upper tail is the probability of a rare event occurring.
The conditional CDF which exceed the threshold t can then be de
ned as
F
ð
x
þ
t
Þ
F
ð
t
Þ
F
t
ð
Þ
¼
ð
8
:
1
Þ
x
for
x
[
0
1
F
ð
t
Þ
