(abridged life table) (radix) q h x 6. l 0 6 q x (1) x (exact age x) : l x, T x, ê x (2)exact age x x + n : n q x,
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1 life table ê x ) complete life table) 5
2 (abridged life table) (radix) q h x 6. l 0 6 q x (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 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
3 p x np x (x ) p x x l x x 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 l x = l x+1 1 l x = L x l x > l x+1 L x (l x + l x+1 ) = L x 5 L x l l 1 = L 0 0.4l l 2 = L 1 0.5l l 3 = L 2 0.5l l 4 = L 3 nl x x l x x + n n 5 1 L x
4 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 q x q x = d x l x
5 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 D x q x D x q x = P x D x = D x P x D x P x h x h x = D x P x h x q x = h x h x q x q x l 0 100,000 q x l 0 q 0 = d o 100, =366 d 0 l 0 d 0 = l 1 100, =99,634
6 4 l x d x 0 4 l 0 5 q 0 = 5 d 0 100, =512 l 0 5 d 0 = l 5 100, =99,488 l 5 l x L x ( ) l x 1 L 0 = 1 24 (l 0 + l 4w ) (l 4w + l 2m ) (l 2m + l 3m ) (l 3m + l 6m ) (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 ) (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, , 000 = ê 10 ê 10 = 6, 715, , 412 =
7 4.2 : 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
8 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 m M 90,t m F 90,t t 89 t 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 = B t, B F t = 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 ) L x 1 3 L 0 99,611 L 1 99, ,489/99,611= , , =697,391 L 2 99, ,436/99,489= , =726,196 x x + 1 L x+1 / x+1 x L x
9 89 90 L x / L x x=90 x=89 3 L 89 26,372 L , ,166/(26, ,166) = , =142, , , = ,435, /206=738,527 1,435, /206=696, L L 0 100, L 0 99, ,611/100, , =694,
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15 45(2033) 7,000 62(2050) 5,838 ( 9) 40(2028) 7,000 61(2049) 5,000 62(2050) 4, (3) (65 ) (65 2,200 25(2013) 3,000 30(2018) 3, (2043) 62(2050 3, (2001) (2020) (2001) (2013) ( (2050) (2006) 62(2050) (2001) (2008) (2014) (2050) (2001) 98 33(2021) ( (2050) 162 1
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