[ ( )]
()
~
ψ (T)
φ2 (n') dn' = Φ2 ψ T .
~
~
Φ1 T ≅ ∫0
(A9)
Consequently,
[ ( )]
()
-
~
~
n = ψ T ≅ Φ 21 Φ1 T ,
(A10)
where Φ 21 is the inverse function of Φ2(n).
-
Since Φ2(n) describes a beta distribution, Φ 21 must be the inverse of a beta dis-
-
tribution. Aivazyan et al. (1983) give
[ ( )] ≅
()
α
^
-
~
~
n T ≅ Φ 21 Φ1 T
[ ( )]
^
α + β exp 2w T ,
(A11)
~
^
where
1
1
1/2
~
()
T h+λ
2
5
~
λ + 6 - 3h ,
wT =
-
-
(A12)
2β - 1 2α - 1
^
^
h
-1
1
1
h = 2
+
^ ,
(A13)
2α - 1 2β - 1
^
~
T2 - 3
λ=
.
(A14)
6
30
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