Συγκριτική...
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13-Apr-2017Category
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e-mail: bozikas@unipi.gr
, 4-7 2016
. , ..
I ( , )
I , 50 (1961-2010): 70.2 78 73.8 83.3
I
I
. , ..
I ( , )
I , 50 (1961-2010):
70.2 78 73.8 83.3
I
I
. , ..
I ( , )
I , 50 (1961-2010): 70.2 78 73.8 83.3
I
I
. , ..
I ( , )
I , 50 (1961-2010): 70.2 78 73.8 83.3
I
I
. , ..
I ( , )
I , 50 (1961-2010): 70.2 78 73.8 83.3
I
I
. , ..
I 3 :
1 2
. , ..
I 3 :1
2
. , ..
I 3 :1 2
. , ..
1
2
3
. , ..
1 2
3
. , ..
1 2
3
. , ..
1 2
3
. , ..
1 2
3
. , ..
I
: Human Mortality Database (2015) x : 60-94 t: 1981-2010 t x ( 5 ): 1887-1891 1946-1950
I
.. : Dx,t : Ex,t() : E 0x,t Ex,t + 1/2 : x,t = dx,t/Ex,t ( mx,t) : qx,t = dx,t/E
0x,t
. , ..
I
: Human Mortality Database (2015) x : 60-94 t: 1981-2010 t x ( 5 ): 1887-1891 1946-1950
I
.. : Dx,t : Ex,t() : E 0x,t Ex,t + 1/2 : x,t = dx,t/Ex,t ( mx,t) : qx,t = dx,t/E
0x,t
. , ..
I Lee and Carter (1992): logx ,t = x + (1)x
(1)t (M1)
I Renshaw and Haberman (2006): logx ,t = x + (1)x
(1)t + tx (M2)
I Cairns et al. (2006): logit qx ,t = (1)t + (x x)
(2)t (M3)
, logit qx,t = logqx,t
1 qx,tI :
x : x
(i)t : t
(1)x : ,
tx : t x
. , ..
I Lee and Carter (1992): logx ,t = x + (1)x
(1)t (M1)
I Renshaw and Haberman (2006): logx ,t = x + (1)x
(1)t + tx (M2)
I Cairns et al. (2006): logit qx ,t = (1)t + (x x)
(2)t (M3)
, logit qx,t = logqx,t
1 qx,tI :
x : x
(i)t : t
(1)x : ,
tx : t x
. , ..
I Lee and Carter (1992): logx ,t = x + (1)x
(1)t (M1)
I Renshaw and Haberman (2006): logx ,t = x + (1)x
(1)t + tx (M2)
I Cairns et al. (2006): logit qx ,t = (1)t + (x x)
(2)t (M3)
, logit qx,t = logqx,t
1 qx,t
I :
x : x
(i)t : t
(1)x : ,
tx : t x
. , ..
I Lee and Carter (1992): logx ,t = x + (1)x
(1)t (M1)
I Renshaw and Haberman (2006): logx ,t = x + (1)x
(1)t + tx (M2)
I Cairns et al. (2006): logit qx ,t = (1)t + (x x)
(2)t (M3)
, logit qx,t = logqx,t
1 qx,tI :
x : x
(i)t : t
(1)x : ,
tx : t x . , ..
I R
I
I M1 M2 :
.. Dx ,t Poisson(Ex ,t x ,t)I M3:
.. Dx ,t Binomial(E 0x ,t , qx ,t)
. , ..
I R
I
I M1 M2 :
.. Dx ,t Poisson(Ex ,t x ,t)I M3:
.. Dx ,t Binomial(E 0x ,t , qx ,t)
. , ..
I R
I
I M1 M2 :
.. Dx ,t Poisson(Ex ,t x ,t)I M3:
.. Dx ,t Binomial(E 0x ,t , qx ,t)
. , ..
I R
I
I M1 M2 :
.. Dx ,t Poisson(Ex ,t x ,t)
I M3:
.. Dx ,t Binomial(E 0x ,t , qx ,t)
. , ..
I R
I
I M1 M2 :
.. Dx ,t Poisson(Ex ,t x ,t)I M3:
.. Dx ,t Binomial(E 0x ,t , qx ,t)
. , ..
I R
I
I M1 M2 :
.. Dx ,t Poisson(Ex ,t x ,t)I M3:
.. Dx ,t Binomial(E 0x ,t , qx ,t)
. , ..
- M1
60 65 70 75 80 85 90 95
4.5
3.5
2.5
1.5
x vs. x
age
60 65 70 75 80 85 90 95
0.00
0.01
0.02
0.03
0.04
x(1)
vs. x
age
1980 1990 2000 2010
86
42
02
4
t(1)
vs. t
year
60 65 70 75 80 85 90 95
54
32
x vs. x
age
60 65 70 75 80 85 90 95
0.01
0.02
0.03
0.04
x(1)
vs. x
age
1980 1990 2000 2010
10
50
5
t(1)
vs. t
year
. , ..
- M2
60 65 70 75 80 85 90 95
4.5
3.5
2.5
1.5
x vs. x
age
60 65 70 75 80 85 90 95
0.015
0.025
0.035
x(1) vs. x
age
1980 1990 2000 2010
64
20
24
t(1)
vs. t
year
1890 1910 1930 19500
.200
.100.0
00.1
0
tx vs. tx
cohort
. , ..
- M2
60 65 70 75 80 85 90 95
4.5
3.5
2.5
x vs. x
age
60 65 70 75 80 85 90 95
0.020
0.030
0.040
x(1) vs. x
age
1980 1990 2000 2010
50
5
t(1)
vs. t
year
1890 1910 1930 19501
.00
.50.0
0.5
tx vs. tx
cohort
. , ..
- M3
1980 1985 1990 1995 2000 2005 2010
3.0
2.9
2.8
2.7
t(1)
vs. t
year
1980 1985 1990 1995 2000 2005 2010
0.096
0.100
0.104
0.108
t(2)
vs. t
year
1980 1985 1990 1995 2000 2005 2010
3.5
3.4
3.3
3.2
3.1
3.0
t(1)
vs. t
year
1980 1985 1990 1995 2000 2005 2010
0.120
0.125
0.130
0.135
0.140
t(2)
vs. t
year
. , ..
1
2
3
. , ..
I
I
I
,
. , ..
- M1
60 65 70 75 80 85 90 95
32
10
12
3
age
resid
uals
1980 1990 2000 2010
32
10
12
3calendar year
resid
uals
1890 1910 1930 1950
32
10
12
3
year of birth
resid
uals
60 65 70 75 80 85 90 95
32
10
12
3
age
resid
uals
1980 1990 2000 2010
32
10
12
3
calendar year
resid
uals
1890 1910 1930 1950
32
10
12
3
year of birth
resid
uals
I
. , ..
- M2
60 65 70 75 80 85 90 95
32
10
12
3
age
resid
uals
1980 1990 2000 2010
32
10
12
3calendar year
resid
uals
1890 1910 1930 1950
32
10
12
3
year of birth
resid
uals
60 65 70 75 80 85 90 95
32
10
12
3
age
resid
uals
1980 1990 2000 2010
32
10
12
3
calendar year
resid
uals
1890 1910 1930 1950
32
10
12
3
year of birth
resid
uals
. , ..
- M3
60 65 70 75 80 85 90 95
32
10
12
3
age
resid
uals
1980 1990 2000 20103
21
01
23
calendar year
resid
uals
1890 1910 1930 1950
32
10
12
3
year of birth
resid
uals
60 65 70 75 80 85 90 95
32
10
12
3
age
resid
uals
1980 1990 2000 2010
32
10
12
3
calendar year
resid
uals
1890 1910 1930 1950
32
10
12
3
year of birth
resid
uals
I ( )I
. , ..
I AIC = 2k 2 log L, k
I AIC (c) = AIC +2k(k + 1)
n k 1, n
I BIC = (log n)k 2 log L
AIC(c) BICM1 -5,472.27 98 11,162(2) 11,623(3)M2 -5,080.40 151 10,516(1) 11,207(1)M3 -5,573.81 60 11,275(3) 11,563(2)
M1 -6,234.97 98 12,687(2) 13,149(2)M2 -5,171.16 151 10,697(1) 11,388(1)M3 -7,923.67 60 15,975(3) 16,263(3)
. , ..
I AIC = 2k 2 log L, k
I AIC (c) = AIC +2k(k + 1)
n k 1, n
I BIC = (log n)k 2 log L
AIC(c) BICM1 -5,472.27 98 11,162(2) 11,623(3)M2 -5,080.40 151 10,516(1) 11,207(1)M3 -5,573.81 60 11,275(3) 11,563(2)
M1 -6,234.97 98 12,687(2) 13,149(2)M2 -5,171.16 151 10,697(1) 11,388(1)M3 -7,923.67 60 15,975(3) 16,263(3)
. , ..
I AIC = 2k 2 log L, k
I AIC (c) = AIC +2k(k + 1)
n k 1, n
I BIC = (log n)k 2 log L
AIC(c) BICM1 -5,472.27 98 11,162(2) 11,623(3)M2 -5,080.40 151 10,516(1) 11,207(1)M3 -5,573.81 60 11,275(3) 11,563(2)
M1 -6,234.97 98 12,687(2) 13,149(2)M2 -5,171.16 151 10,697(1) 11,388(1)M3 -7,923.67 60 15,975(3) 16,263(3)
. , ..
I AIC = 2k 2 log L, k
I AIC (c) = AIC +2k(k + 1)
n k 1, n
I BIC = (log n)k 2 log L
AIC(c) BICM1 -5,472.27 98 11,162(2) 11,623(3)M2 -5,080.40 151 10,516(1) 11,207(1)M3 -5,573.81 60 11,275(3) 11,563(2)
M1 -6,234.97 98 12,687(2) 13,149(2)M2 -5,171.16 151 10,697(1) 11,388(1)M3 -7,923.67 60 15,975(3) 16,263(3)
. , ..
I M1 M2 (M1 M2)
I H0 : M1 M2H1 : M2
I LR = 2 logL2
L1( 2(n2n1),)
