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Verification
.
Nelsen10Order
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Imports
Init
Verification.Nelsen10Dependence
Verification.SchurOrthantEquivalence
Copula.Order.SymmetricSchur
Imported by
Verification
.
n10Half
Verification
.
n10Low
Verification
.
n10High
Verification
.
nelsen10_crossing_low
Verification
.
nelsen10_crossing_high
Verification
.
nelsen10_orthant_incomparable
Verification
.
nelsen10_schur_incomparable
Verification
.
nelsen10_schurBoth_incomparable
← Mathematical handbook
source
noncomputable def
Verification
.
n10Half
:
↑
unitInterval
Equations
Verification.n10Half
=
⟨
1
/
2
,
Verification.n10Half._proof_2
⟩
Instances For
source
noncomputable def
Verification
.
n10Low
:
↑
unitInterval
Equations
Verification.n10Low
=
⟨
1
/
16
,
Verification.n10Low._proof_2
⟩
Instances For
source
noncomputable def
Verification
.
n10High
:
↑
unitInterval
Equations
Verification.n10High
=
⟨
9
/
16
,
Verification.n10High._proof_2
⟩
Instances For
source
theorem
Verification
.
nelsen10_crossing_low
:
(
nelsen10
n10Half
)
.
cdf
![
n10Low
,
n10Low
]
<
(
nelsen10
1
)
.
cdf
![
n10Low
,
n10Low
]
source
theorem
Verification
.
nelsen10_crossing_high
:
(
nelsen10
1
)
.
cdf
![
n10High
,
n10High
]
<
(
nelsen10
n10Half
)
.
cdf
![
n10High
,
n10High
]
source
theorem
Verification
.
nelsen10_orthant_incomparable
:
¬
(
nelsen10
n10Half
)
.
LowerOrthantLE
(
nelsen10
1
)
∧
¬
(
nelsen10
1
)
.
LowerOrthantLE
(
nelsen10
n10Half
)
source
theorem
Verification
.
nelsen10_schur_incomparable
:
¬
(
nelsen10
n10Half
)
.
SchurLE
(
nelsen10
1
)
∧
¬
(
nelsen10
1
)
.
SchurLE
(
nelsen10
n10Half
)
source
theorem
Verification
.
nelsen10_schurBoth_incomparable
:
¬
(
nelsen10
n10Half
)
.
SchurBothLE
(
nelsen10
1
)
∧
¬
(
nelsen10
1
)
.
SchurBothLE
(
nelsen10
n10Half
)