Documentation
Verification
.
TwoStripRank
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Imports
Init
Verification.TentArea
Verification.TwoStrip
Copula.Rank.Concordance
Copula.Rank.Symmetry
Imported by
Verification
.
continuous_medianWedge
Verification
.
integral_medianWedge
Verification
.
rho_twoStrip
Verification
.
twoStrip_mix_reflect_first
Verification
.
concordanceQ_reflect_first_self
Verification
.
tau_twoStrip
← Mathematical handbook
Rho and tau of arbitrary two-strip displacements
#
source
theorem
Verification
.
continuous_medianWedge
:
Continuous
medianWedge
source
theorem
Verification
.
integral_medianWedge
:
∫
(
u
:
↑
unitInterval
)
,
medianWedge
u
=
1
/
4
source
theorem
Verification
.
rho_twoStrip
(
g
:
StripDisplacement
)
:
(
twoStrip
g
)
.
spearmanRho
=
3
*
∫
(
v
:
↑
unitInterval
)
,
g
.
toFun
v
source
theorem
Verification
.
twoStrip_mix_reflect_first
(
g
:
StripDisplacement
)
:
(
twoStrip
g
)
.
mix
(
(
twoStrip
g
)
.
reflect
{
0
}
)
ProbabilityTheory.Copula.unitHalf
=
ProbabilityTheory.Copula.independence
2
source
theorem
Verification
.
concordanceQ_reflect_first_self
(
C
:
ProbabilityTheory.Copula
2
)
:
C
.
concordanceQ
(
C
.
reflect
{
0
}
)
=
0
source
theorem
Verification
.
tau_twoStrip
(
g
:
StripDisplacement
)
:
(
twoStrip
g
)
.
kendallTau
=
2
*
∫
(
v
:
↑
unitInterval
)
,
g
.
toFun
v