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.
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Init
Copula.Families.AMH
Copula.Order.Rank
Imported by
ProbabilityTheory
.
Copula
.
lowerOrthantLE_amh_iff
← Mathematical handbook
Exact lower-orthant parameter ordering of Ali–Mikhail–Haq copulas
#
source
theorem
ProbabilityTheory
.
Copula
.
lowerOrthantLE_amh_iff
{
θ
η
:
ℝ
}
(
hθmin
:
-
1
≤
θ
)
(
hθmax
:
θ
≤
1
)
(
hηmin
:
-
1
≤
η
)
(
hηmax
:
η
≤
1
)
:
(
amh
θ
hθmin
hθmax
)
.
LowerOrthantLE
(
amh
η
hηmin
hηmax
)
↔
θ
≤
η
AMH copulas are ordered by their parameters, with no missing comparisons.