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Verification
.
Nelsen18Dependence
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Imports
Init
Verification.MTP2ConditionalIncreasing
Verification.Nelsen18
Copula.TailDependence.Basic
Imported by
Verification
.
nelsen18_zero_diagonal
Verification
.
nelsen18_not_pqd
Verification
.
nelsen18_not_ci
Verification
.
nelsen18_not_density_tp2
Verification
.
nelsen18_lowerTail
← Mathematical handbook
source
theorem
Verification
.
nelsen18_zero_diagonal
(
θ
:
ℝ
)
(
hθ
:
2
≤
θ
)
:
∃ (
q
:
↑
unitInterval
),
0
<
q
∧
(
nelsen18
θ
hθ
)
.
cdf
![
q
,
q
]
=
0
source
theorem
Verification
.
nelsen18_not_pqd
(
θ
:
ℝ
)
(
hθ
:
2
≤
θ
)
:
¬
(
nelsen18
θ
hθ
)
.
IsPQD
source
theorem
Verification
.
nelsen18_not_ci
(
θ
:
ℝ
)
(
hθ
:
2
≤
θ
)
:
¬
(
nelsen18
θ
hθ
)
.
IsCI
source
theorem
Verification
.
nelsen18_not_density_tp2
(
θ
:
ℝ
)
(
hθ
:
2
≤
θ
)
:
¬
(
nelsen18
θ
hθ
)
.
HasMTP2Density
source
theorem
Verification
.
nelsen18_lowerTail
(
θ
:
ℝ
)
(
hθ
:
2
≤
θ
)
:
(
nelsen18
θ
hθ
)
.
HasLowerTailDependence
0