Civil Engineering Reference
In-Depth Information
seismic loss samples generated from the earthquake-engineering-based
model. The input seismic loss samples are generated for a period of 100 000
years. Both marginal distribution fi tting and copula function fi tting for
several pairs of groups have been carried out. For illustration, seismic loss
data
L
A
for Groups 2 and 3 are focused on. (The insurance policy, as in
Equation [28.16], is not applied for the base case.) For marginal distribution
modelling, results for Group 2 (which will be discussed in the following)
are generally applicable to other groups, because the building portfolio is
statistically equivalent and seismic hazard characteristics do not vary sig-
nifi cantly for the six groups.
The fi rst step is to determine a suitable value of the threshold
above
which seismic loss data can be approximated by the GP model. Two diag-
nostic tools, mean excess plot and shape parameter plot, are employed, and
the results for Group 2 are presented in Fig. 28.4. Figure 28.4a shows that
the trend of mean excess plot is increasing and a linear straight line can be
fi tted for seismic loss data exceeding a threshold of about 4-5 million CAD.
Figure 28.4b indicates that the shape parameter
μ
is gradually decreasing
as the threshold level increases. For very large threshold values, the mean
excess plot becomes fl at (Fig. 28.4a), while the shape parameter approaches
zero (Fig. 28.4b). These results indicate that the degree of heavy right tail
becomes less extensive. (Note that the reliability of such diagnostic analyses
decreases with the threshold
ξ
, because the number of used data points
decreases rapidly.) On the other hand, it should also be reminded that these
diagnostic tools provide loose guidance on the adequate level of
μ
only
(Cebrian
et al.
, 2003; McNeil
et al.
, 2005); the fi nal decision should be made
μ
20
1. 5
Group 2
Group 2
0.99
0.98
0.998
0.995
0.998
0.98
0.99
0.995
15
1. 0
Mean and 90%
confidence interval
10
0.5
5
0.0
Threshold based on
annual maximum
seismic loss
30
Threshold based on
annual maximum
seismic loss
0
-0.5
0
10
20
40
0
5
10
15
Threshold (10
6
CAD)
Threshold (10
6
CAD)
(a)
(b)
28.4
(a) Mean excess plot for Group 2, and (b) shape parameter plot
for Group 2.
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