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0.04
0.04
Empirical copula
Normal copula
r
= 0.729
0.03
0.03
0.02
0.02
0.01
0.01
0.0
0.0
1.0
1.0
0.5
0.5
u
2
u
2
1.0
1.0
0.5
0.5
0.0
0.0
0.0
0.0
u
1
u
1
(a)
(b)
0.04
Gumbel copula
q
= 2.272
0.04
HRT copula
q
= 2.306
0.03
0.03
0.02
0.02
0.01
0.01
0.0
0.0
1.0
1.0
0.5
0.5
u
2
u
2
1.0
1.0
0.5
0.5
0.0
0.0
u
1
u
1
0.0
0.0
(c)
(d)
28.8
Comparison of copula density plots using joint POT data for
Groups 2 and 3: (a) empirical copula, (b) normal copula, (c) Gumbel
copula, and (d) HRT copula.
separation distance (i.e. different pairs of groups); it becomes very high for
short separation distance (e.g.
0.9 when two portfolios overlap), and
decreases gradually as the separation distance increases. In addition, Fig.
28.9 includes results for insurance seismic loss data (i.e. samples are obtained
by applying Equation [28.16] with
D
τ
=
1.0). The same
tendency is seen for original seismic loss data and insurance seismic loss
data.
Finally, to verify the capability and accuracy of the proposed statistical
method, seismic loss samples for Groups 2 and 3 as well as Groups 2 and
5 are generated by using the fi tted GP marginal distributions and the copula
functions. Then, the combined seismic loss samples are computed by adding
the samples for two groups (i.e. portfolio aggregation), and are used for
=
0.1,
C
=
0.5, and
γ
=
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