Construction of a dynamic life table based on the Algerian retired population mortality experience

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t= [2004,2013]
Dt
x,x+5
lx,t

mxt

x, x + 5
t Mt
x,x+5,x, x + 5
t Dt
x,x+5
Lt
x,x+5 Mt
x,x+5 =Dt
x,x+5
Lx,x+5
Lt
x,x+5
t
Lt
x,x+5 =lt−1
x,x+5+lt
x,x+5
2
x∈[45 −95[
t= 2004,2005, ...2013
[x, x + 5[ t

Mt
x,x+5)

mx+2,5,t
Mt
x,x+5
mx+2,5,t =Mt
x,x+5 mx+0,5;t
x= 50,51,52, ...., 84
mx+2,5t
ln(c
mx+2,5,t) = a+b(x+ 2,5) + c(x+ 2,5)2
minW SE =
75
X
x=50,55
Dt
x,x+5 ∗(mx+2,5,t −ˆa−ˆ
b(x+ 2,5) −ˆc(x+ 2,5)2)

ln(mxt)
x t

t x
mB
x,t =qmm
x,t.mf
x,t
B m :f:
Rx,t =v
u
u
tmm
x,t
mf
x,t

mm
x,t =mB
x,t.Rx,t mf
x,t =mB
x,t
Rx,t
mB
x,t Rx,t
x t
ln(mB
x,t) = αx+βx∗κt+ξx,t
M inW SS E(1) =
79
X
x=50
2014
X
t=1977
Wx,t[ln(mx,t)−ˆαx−ˆ
βx∗ˆκt]2
Wx,t t x
Pˆ
βx= 1 Pˆκt= 0

Rx,t =Ax+Bx∗Kt+εx,t
M inW SS E(2) =
79
X
x=50
2014
X
t=1977
Wx,t[Rx,t −ˆ
Ax−ˆ
Bx∗ˆ
Kt]2
Pˆ
Bx= 1 Pˆ
Kt= 0
κtKt
κt
κt=κt−1+u+εtu εt

st
κt=λ.κt−1+u+εtu
κt
κt−κt−1
κt−κt−1=λ.(κt−1−κt−2) + u+εt
κt−κt−1= (1 + λ).κt−1−λ.κt−2+u+εt
(Kt)
Kt
Kt
κtKt
ln(c
mB
x,t) = b
αx+b
βx∗b
κtb
αxb
βx
b
κt
b
Rx,t
b
Rx,t =b
Ax+b
Bx∗c
Ktb
Ax,b
Bx
c
Kt
mm
x,t =mB
x,t.Rx,t mf
x,t =mB
x,t
Rx,t

ˆmx= ˆmx−1exp(P80 +s.(x−80)) x= 80,81,82, .....
P80 s
s mm
110 = 1
mf
110 = 0.8
ln(mx) = a+b(x−79) + c(x−79)2+ξx

mref
x,t x t
mexp
x,t
mref
x,t mexp
x,t
Logit(mexp
x,t ) = γ+δLogit(mref
x,t ) + ζx,t
γ δ ζx,t
MinSS E =
79
X
x=50
2013
X
t=2004
[Logit(c
mexp
x,t )−γ−δLogit(mref
x,t )]2

Logit[mexp
xt ]Logit[mref
xt ]
¯
Dx,x+n[x, x +
n[¯
Lx,x+n
¯
Mx,x+n=¯
Dx,x+n
¯
Lx,x+n
c
Dx,x+n=c
Mx,x+n.¯
Lx,x+nc
Mx,x+n
[x, x +n[
x, x + 1, x + 2, ..., x + 4
c
Mx,x+n=
x+n−1
Y
z=x
mz

1−αc
Mx,x+n
1−α
P(Mx,x+n∈[c
Mx,x+nµα
2
v
u
u
tc
Mx,x+n(1 −c
Mx,x+n)
b
Lx,x+n
], x =x1) = 1 −α
µα
2
α
2
1−αc
Mx,x+n
1−β G
1−β= (1 −α)G
P(Mx,x+n∈[c
Mx,x+nµβ
2
v
u
u
tc
Mx,x+n(1 −c
Mx,x+n)
b
Lx,x+n
], x∈[x1, xG]) = 1 −α

nd
Logit(c
mexp
x,t ) = η+χLogit(mref
x,t ) + ϕLogit(mref
x,t )2+ζx,t
η χ ϕ ζ