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J M I
Aj
F j
pj
X j
q ∗ijt
q ∗i0t
dijt
U ijt(q ijt,i0t) = ci
1
bi
dijtq ijt −
(q 2ijt + d2ijt)
2
+ q i0t
+ ς ijt,
bi, ci, dijt > 0, dijt < ∞,
ci bi
q ijt
ς ijt
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yit = q i0t + F j + Aj + (q ijt − q̃ j)I qijt≥q̃j pj,
yit I qijt≥q̃j
q̃ j
q ∗ijt =
dijt dijt ≤ q̃ j
dijt − bi pj dijt − bi pj > q̃ j
q̃ j
dijt − bi pj ≤ q̃ j ≤ dijt .
•
q 2P ;PPU ∗ijt =
0 dijt ≤ bi pj
dijt − bi pj dijt > bi pj
•
q 3P ∗ijt =
dijt dijt ≤ q̃ j
dijt − bi pj
dijt − bi pj > q̃ j
q̃ j dijt − bi pj ≤ q̃ j ≤ dijt .
•
q FR∗ijt = dijt .
V 3P ijt (yit, pj , F j) =
ci(yit − F j − Aj) + ς ijt q ∗ijt ≤ q̃ j
ci
yit − F j − Aj + pj q̃ j . . .
−
dijt − bi pj2
pj
+ ς ijt q ∗ijt > q̃ j ,
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V 2P ijt (yit, pj , F j) =
ci(yit − F j) + ς ijt
q ∗ijt = 0
ci
yit − F j −
dijt −
bi pj2
pj
+ ς ijt q ∗ijt > 0
V PPU ijt (yit, pj , F j) =
ci(yit) + ς ijt q ∗ijt = 0
ci
yit −
dijt −
bi pj2
pj
+ ς ijt
q ∗ijt > 0
V FRijt (yit, pj , F j) = ci(yit − F j − Aj) + ς ijt
• SC T jt
• I P j
•
X
J × K
• Z il
I × L
• IT J ×M
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• ADijt
ADijt ADijt
κij
τ ij
ς ijt
ς ijt = ρ1SC T jt × I T j + ρ2I P j + I T jmΛmi + X jkζ U k + Z ilξ U l + κijADijt + ijt ,
ijt
ρ1
ρ2 Λ
ΣΛ Λmi
ζ U ξ U
Φit
Φit
ht
ηi
ηi
µη, σ2η
dijt = Φit exp(htat + I T jm∆mi + X jkζ Dk + Z ilξ Dl + τ ijADijt + ηi),
a ∆
∆
Σ∆
ζ D
ξ D
X Z
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Φit
E [V ijt ] = P (q ∗ijt ≤ q̃ j)E
V ijt|q
∗ijt < q̃ j
+ P (q
∗ijt > q̃ j)E
V ijt |q
∗ijt > q̃ j
,
•
E
V 3P ijt
= P (q ∗ijt < q̃ j)ci(yit − F j − Aj) + P (q ∗ijt > q̃ j)×
ci
yit − F j − Aj +
1
2bi p
2j − E (Φit exp(htat + I T jm,3P ∆3P,i . . .
+ X jkζ Dk + Z ilξ Dl + τ ijADijt + ηi|q ∗ijt > q̃ j) pj
+ ς ijt ,
•
E
V 2P ijt
= P (q ∗ijt = 0j)ci(yit − F j) + P (q ∗ijt > 0)×
ci
yit − F j +
1
2bi p
2j − E (Φit exp(htat + I T jm,2P ∆2P,i . . .
+ X jkζ Dk + Z ilξ Dl + τ ijADijt + ηi|q ∗ijt > 0) pj
+ ς ijt
•
E
V PPU ijt
= P (q ∗ijt = 0j)ci(yit) + P (q ∗ijt > 0)×
ci
yit +
1
2bi p
2j − E (Φit exp(htat + I T jm,PPU ∆PPU,i . . .
+ X jkζ Dk + Z ilξ Dl + τ ijADijt + ηi|q ∗ijt > 0) pj
+ ς ijt ,
•
E
V FRijt
= ci(yit − F j − Aj) + ς ijt .
E [V i0t] = ciyit + ς i0t.
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Bj,q j q Bk,q
k
J j
BV Meanj =
1
J − 1
1
maxj,k;j=k
q̄
q=0(Bj,q − Bk,q)2 ×
J k=1;k=j
q̄q=0
(Bj,q − Bk,q)2,
1maxj,k;j=k[
q̄q=0
(Bj,q−Bk,q)2] q̄
BV Medianj = k;k=j
1
maxj,k;j=k
q̄
q=0(Bj,q − Bk,q)2 ×
J k=1;k=j
q̄q=0
(Bj,q − Bk,q)2
.
j
DIS j =
BV Mean
j +
BV Median
j2
.
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