1 2 2.1 2.2 3 life table ê x ) complete life table) 5
(abridged life table) 3.1 3.1.1 1. 2. (radix) 10 3. 4. 5. q h x 6. l 0 6 q x 3.1.2 2 (1) x (exact age x) : l x, T x, ê x (2)exact age x x + n : n q x, n p x, n L x, n d x n 1 5 q x nq x nq x nq x n p x np x n n q x nq x (x ) q x q x x x x + 1 1 x l x 1 d x l x q x = d x 1 n ( 5 ) nq x l x n q x = n d x
p x np x (x ) p x x l x x + 1 1 1 q x = p x l x+1 /l x = p x n 1 n p x = n q x l x (x x ) l x+n /l x = n p x (0 )l 0 100,000 l 0 = 100, 000 l x l x+1 = d x (l x l x+n = n d x ) l x p x = l x+1 (l x n p x = l x+n ) L x nl x (x ) L x x l x x + 1 1 1 1 l x = l x+1 1 l x = L x l x > l x+1 L x 1 1 2 (l x + l x+1 ) = L x 5 L x 5 1 0.3l 0 + 0.7l 1 = L 0 0.4l 1 + 0.6l 2 = L 1 0.5l 2 + 0.5l 3 = L 2 0.5l 3 + 0.5l 4 = L 3 nl x x l x x + n n 5 1 L x
5 n 2 (l x + l x+n ) = n L x 5L x = L x + L x+1 + L x+2 + L x+3 + L x+4 T x (x ) T x x l x L x = T x ê x (x ) x L x + T x+1 = T x ê x x l x T x l x = ê x ê 0 T 0 = ê 0 l 0 T 0 100, 000 = ê 0 (life expectancy at birth) x x n p x = n L n+x nl x n q x = n L x n L x+n nl x l x L x nl x 3.2 3.2.1 q x q x = d x l x
x (exact age x) E x x + 1 D x q x = D x E x x P x x D x E x D x P x = E x 1 2 D x E x = P x + 1 2 D x q x D x q x = P x + 1 2 D x = D x P x 1 + 1 2 D x P x h x h x = D x P x h x q x = 1 + 1 2 h x h x q x q x 3.2.2 1 l 0 100,000 q x l 0 q 0 = d o 100,000 0.00366=366 d 0 l 0 d 0 = l 1 100,000 366=99,634
4 l x d x 0 4 l 0 5 q 0 = 5 d 0 100,000 0.00512=512 l 0 5 d 0 = l 5 100,000 512=99,488 l 5 l x L x ( ) l x 1 L 0 = 1 24 (l 0 + l 4w ) + 1 24 (l 4w + l 2m ) + 1 24 (l 2m + l 3m ) + 1 8 (l 3m + l 6m ) + 1 4 (l 6m + l 1 ) l 4w : 4 l 2m : 2 l 3m : 3 l 6m : 6 1 L x = 1 2 (l x + l x+1 ) + 1 24 (d x+1 d x 1 ) 5 L x T x L 100+ =1,171 T 100 5L 95 + T 100 =10,303+1,171=11,474 T 95 5 L 0 + T 5 =497,884+7,212,247=7,710,131 T 0 T 4 1 L 4 + T 5 T 3, T 2, T 1, T 0 T x lx = ê x ê x ê 0 ê 0 = 7, 710131 100, 000 = 77.10 ê 10 ê 10 = 6, 715, 007 99, 412 = 67.55 4 4.1
4.2 : 1 7 1 4.3 M x,t = t x F x,t = t x M 90,t F 90,t B t = t t + 1 B M t = t t + 1 B F t = t t + 1 p M x,t = t x 1 t + 1 x p F x,t = t x 1 t + 1 x p M 0,t t t + 1 t + 1 pf 0,t p M 90,t t t + 1 pf 90,t
b x,t = t t + 1 x m M x,t = t x 1 t + 1 x m F x,t = t x 1 t + 1 x m M 0,t m F 0,t t t + 1 t + 1 0 m M 90,t m F 90,t t 89 t + 1 90 t + 1 t M x,t+1 = ( p M x,t + m M x,t)m x 1,t, 1 x 89, F x,t+1 = ( p F x,t + m F x,t)f x 1,t, 1 x 89, B t = 49 x=15 (F x,t + F x,t+1 )b x,t /2, B M t = 106 206 B t, B F t = 100 206 B t, M 0,t+1 = ( p M 0, t + m M 0,t)B M t, F 0,t+1 = ( p F 0, t + m F 0,t)B F t, M 90,t+1 = ( p M 90,t+1 + m M 90,t)(M 89,t + M 90,t ) F 90,t+1 = ( p F 90,t+1 + m F 90,t)(F 89,t + F 90,t ) 4.4 1 L x 1 3 L 0 99,611 L 1 99,489 0 1 99,489/99,611=0.99878 1985 0 698,246 1986 1 698,246 0.99878=697,391 L 2 99,436 1 2 99,436/99,489=0.99947 2 726,583 0.99947=726,196 x x + 1 L x+1 / x+1 x L x
89 90 L x / L x x=90 x=89 3 L 89 26,372 L 90 104,166 89 90 104,166/(26,372+104,166) =0.79797 1986 90 1985 89 178,267 0.79797=142,253 1 0 0 698,246 0.00053 698,246 0.00053= 370 370 4.5 1985 10 1 15 49 1986 15 49 1985 10 1986 9 4 15 1985 10 1 93 6198 1986 10 1 96 5955 95 1076.5 15 0.00013 1985 10 9 1 124 49 143 5250 10 9 1 1985 100 106 100 106 1,435,250 106/206=738,527 1,435,250 100/206=696,723 4.6 0 0 10 9 0 L 0 10 0 0 L 0 100, 000 3 L 0 99,611 0 99,611/100,000 0.99611 696,723 0.99611=694,013 4.7
4.8 1,000 15 1,000 1 1) 5 1947 15 1948 16 1949 17 1948 15 1949 16 1950 17 5 2 1947 15 6 1947 15 1981 49 2.04 1948 15 1954 15 2.05 2.02 2.01 2.03 2.02 2.09 2.05 1988 1954 15 1989 15 3 49 1955 15 49 1956 48 49 1968 36 1980 24 15 1968 15 1989 2.08 2.00 1.95 6 1988 35 1.931 49
2.08 2.08-1.931=0.149 2.00 2.00-1.931=0.069 1.95 1.95-1.931=0.019 3 7 2.08 35 2.08 35 36 36 34 35 1968 1989 2.00 1989 2.30 1990 2.23 1991 2.17 1992 2.12 2000 2.00 1 2.08 2 2 A: B: A: B: 2.00 25 29 50 25 29 2.00 0.5=0.2000 4.9 5 A:
B: A: (a) 2050 (b) (c) B: 50 3 1 A: B: A: B: 1 2
5 5.1 12 2000 1 2,693 18 2006 1 2,774 25 2013 62 2050 1 60 8 4 21 2009 1 2,815 62 2050 1 825 9 4 16 2004 1 2,748 62 2050 9,203 10 4 1970 2.08 5.2 3 (1) (0 14 ) 48 (1973) 209 12(2000) 119 0 14 ) 1980 2,700 12(2000) 1,851 2003 1,700 ( 8 5) 28(2016) 1,600 2050 1,084 62(2050) 1,400 9 1,800 26(2014) 1,500 750 10 (2) (15 64 ) 15 64 7(1995) 8,717 12(2000) 8,638 7(1995) 42(2030) 7,000 62(2050 5,389 ( 8 5
45(2033) 7,000 62(2050) 5,838 ( 9) 40(2028) 7,000 61(2049) 5,000 62(2050) 4,868 10 (3) (65 ) (65 2,200 25(2013) 3,000 30(2018) 3,417 8 5 22 24 65 55(2043) 62(2050 3,586 9 10 5.3 13(2001) 7.7 32(2020) 16.2 11 13(2001) 9.4 25(2013) 8.0 47(2035 7.0 62(2050) 6.7 12 2001 1.7 18(2006) 62(2050) 9.5 12(2001) 119 20(2008) 110 26 (2014) 100 62(2050) 67 11 12(2001) 98 33(2021) 151 50(2038 170 62(2050) 162 1
6 1989 6 1990 12