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Verification
.
Nelsen21Order
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Imports
Init
Verification.Nelsen21Comparison
Copula.Order.Orthant
Imported by
Verification
.
n21Comparison_inv
Verification
.
n21Comparison_psi
Verification
.
nelsen21_lowerOrthant_monotone
← Mathematical handbook
source
theorem
Verification
.
n21Comparison_inv
{
θ
η
:
ℝ
}
(
hθ
:
1
≤
θ
)
(
hη
:
1
≤
η
)
(
u
:
↑
unitInterval
)
:
n21Comparison
θ
η
(
(
n21Generator
θ
hθ
)
.
invFun
u
)
=
(
n21Generator
η
hη
)
.
invFun
u
source
theorem
Verification
.
n21Comparison_psi
{
θ
η
t
:
ℝ
}
(
hθ
:
1
≤
θ
)
(
hη
:
1
≤
η
)
(
ht
:
t
∈
Set.Icc
0
1
)
:
n21Psi
η
(
n21Comparison
θ
η
t
)
=
n21Psi
θ
t
source
theorem
Verification
.
nelsen21_lowerOrthant_monotone
{
θ
η
:
ℝ
}
(
hθ
:
1
≤
θ
)
(
hθη
:
θ
≤
η
)
:
(
nelsen21
θ
hθ
)
.
LowerOrthantLE
(
nelsen21
η
⋯
)