Civil Engineering Reference
In-Depth Information
a)
N short term independent realisations
b)
The distribution of extremes
Fig. 2.9
Distribution of extreme values
Let therefore
(
)
f
x
T
(2.38)
κ =
⋅
max
(
)
be an ensemble variable signifying the event that
x
0
≤≤
tT
exceeds a given value
κ occurs only once within each realisation is an event that
coincides with the occurrence of
ma
x
, i.e. they are simultaneous events. They are rare
events at the tail of the peak distribution given in Eq. 2.36, and for the statistics of such
events it is a reasonable assumption that they will also comply to an exponential
distribution, i.e. that
x
. The probability that
max
