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Verification
.
DeterministicRho
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Imports
Init
Verification.CenteredProperties
Verification.Mixture
Imported by
Verification
.
centralW_rho
Verification
.
deterministic_rho_attained
← Mathematical handbook
Every rho is attained at xi=1 by a radially symmetric copula
#
source
theorem
Verification
.
centralW_rho
(
α
:
↑
unitInterval
)
:
(
centralW
α
)
.
spearmanRho
=
1
-
2
*
↑
α
^
3
source
theorem
Verification
.
deterministic_rho_attained
(
r
:
ℝ
)
(
hr
:
r
∈
Set.Icc
(-
1
)
1
)
:
∃ (
C
:
ProbabilityTheory.Copula
2
),
C
.
IsRadiallySymmetric
∧
C
.
chatterjeeXi
=
1
∧
C
.
spearmanRho
=
r