研究シリーズ 第34号
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- かずし しばもと
- 7 years ago
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1 personal income distribution 64
2 life stage 4134 (R.E.Mouer)
3
4
5
6 (1) (2)
7 (1) (2) (3) (4) (5) (6) (21) (21) (11) (21) (21) (16) (11) (13) (16) (16) (14) (16) (16) (14) (16) (12) (13) (16) (16) (16) (16) (16) (16) (16) (16) (16) (13) (19) (16) (15) (16) (15) (? ) (16) (14) (16) (16) (16) (16) (16) (16) (16) (16) (16) (13) (16) (16) (16) (16) (17) (16) (16) (15) (16) (16) 1. (1) (2)(3) 3. (4) 4. (5) (6)
8
9 (6) Atkinson 2 39 Sen
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11
12
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14 lognormal distribution R.Gibrat positive skewness normal distribution x μ σ 2 11 f (x) 9 Gibrat R stochastic process stochastic theory Champernowne D.G Aitchison.J and Brown J.A.C. 1 77
15 34 ( ) 39 ( ) ( ) ( ) ( ) ( ) %( %) %( %) %( %) %( %) ( 1.8) 0.6( 0.6) ( 0.0) 0.0( 0.0) ( 4.4) 6.1( 6.7) ( 1.5) 1.1( 1.1) ( 10.2) 11.6( 18.2) ( 7.1) 6.4( 7.6) ( 21.6) 13.2( 31.4) ( 18.1) 12.7( 20.5) ( 37.2) 12.4( 43.8) ( 34.4) 15.5( 35.7) ( 52.5) 10.6( 54.4) ( 51.4) 14.9( 50.6) ( 64.9) 8.8( 63.2) ( 65.1) 12.6( 63.2) ( 74.3) 7.1( 70.3) ( 74.9) 9.9( 73.2) ( 81.3) 5.7( 76.0) ( 82.0) 7.5( 80.6) ( 86.0) 4.5( 80.5) 900 1, ( 86.8) 5.5( 16.1) ( 91.7) 6.5( 87.0) 1,000 1, ( 92.6) 6.8( 92.9) ( 95.0) 4.2( 91.2) 1,200 1, ( 95.8) 3.4( 96.3) ( 96.9) 2.7( 93.9) 1,400 1, ( 92.3) 1.8( 98.1) ( 98.0) 1.8( 95.8) 1,600 1, ( 98.4) 0.9( 99.0) 900 1, ( 98.6) 1.2( 97.0) 1,800 2, ( 99.0) 0.5( 99.4) 1, (100.0) 3.0(100.0) 2, (100.0) 0.6(100.0) (0.9915) (0.9996) 78
16 44 49 ( ) ( ) ( ) ( ) %( %) %( %) %( %) %( %) ( 0.2) 0.1( 0.1) ( 0.6) 0.0( 0.0) ( 1.1) 0.8( 0.9) ( 1.8) 0.9( 0.9) ( 3.1) 2.5( 3.3) ( 4.5) 3.7( 4.7) ( 7.2) 4.9( 8.2) ( 10.0) 7.7( 13.4) ( 14.0) 7.3( 15.5) ( 19.2) 10.9( 23.2) ( 24.4) 9.0( 24.4) ( 31.9) 12.3( 35.5) ( 34.0) 9.8( 34.2) ( 45.7) 12.1( 37.6) 900 1, ( 44.6) 9.8( 44.0) ( 58.4) 10.9( 58.5) 1,000 1, ( 62.1) 17.5( 61.5) ( 69.1) 9.2( 67.7) 1,200 1, ( 75.8) 13.3( 74.7) ( 77.7) 7.5( 75.2) 1,400 1, ( 84.0) 9.2( 83.9) ( 83.7) 6.0( 81.2) 1,600 1, ( 89.5) 6.0( 89.9) ( 88.3) 4.6( 85.8) 1,800 2, ( 92.8) 3.8( 93.7) ( 91.2) 3.5( 89.4) 2,000 2, ( 97.7) 4.4( 98.1) ( 93.4) 2.7( 92.0) 2,500 3, ( 99.4) 1.3( 99.4) ( 96.9) 4.1( 96.1) 3, (100.0) 0.6(100.0) ( 98.5) 2.0( 98.1) (100.0) 1.9(100.0) (0.9999) (0.9986) 79
17 ( ) ( ) % % % % ( 0.0) 0.0 ( 0.0) ( 0.0) 0.0 ( 0.0) ( 0.0) 0.0 ( 0.0) ( 0.1) 0.0 ( 0.0) ( 0.1) 0.1 ( 0.1) ( 0.5) 0.4 ( 0.4) ( 1.3) 1.1 ( 1.5) ( 3.4) 2.2 ( 3.7) ( 7.2) 3.6 ( 7.3) ( 12.6) 5.0 ( 12.3) ( 19.0) 6.2 ( 18.5) ( 32.9) 14.6 ( 33.1) l4.2 ( 47.2) 14.9 ( 48.0) ( 60.8) 13.2 ( 61.2) ( 72.4) 10.7 ( 71.9) ( 81.0) 8.2 ( 80.1) ( 91.3) 10.3 ( 90.4) ( 95.8) 5.1 ( 95.4) ( 97.9) 2.4 ( 97.9) ( 98.9) 1.1 ( 99.0) ( 99.3) 0.5 ( 99.5) (100.0) 0.5 (100.0) (1.0000)
18 f ( x) = exp{ ( x μ) } 2 2πσ 2σ F(x) 3 2 F( x) = x f ( t) dt y x = l n y y y G( y) = f ( t) dt 0 t G(y) y μ σ (i) y i x μ y i x σ ( j) y j μ ' ( μ ) σ ' ( σ ) Z 2 t 3 5 ERF( Z) = e dt π 0 l y μ 3 6 Z = n 2σ d Z = dy y 2σ G ( Z) = + ERF( Z)
19 logarithmic probability graph S ( x ) 16 S 82
20
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23 86
24 ( 18) 87
25 ( l Y n / H (G ) ( b 1 ) ( b 2,b3 ) G = b b b3 ( 1.69) ( 0.93) ( 3.28) ( 2.74) R 2 = S. E. = D. W. =
26 ( 1 ) ( ) ( 2 ) ( ) ( 3 ) ( ) ( 4 ) ( ) ( 5 ) ( ) (27) (27) (27) (27) (27) (27) (29) (29) (29) (29) (29) (29) (14) (18) (18) (13) (13) (18) (18) (13) (13) (18) (18) (13) (13) (23) (23) (13) (13) (23) (23) (12) (12) (22) (22) (12) (12) (18) (22) (22) (12) (12) (18) (22) (22) (12) (12) (18) (22) (22) (11) (11) (18) 48 *0.2176(23) *0.1772(23) (12) (12) (18) 49 *0.2132(23) *0.1746(23) (11) (11) (18) 50 *0.2081(23) *0.1761(23) (12) (12) (18) 51 *0.2070(24) *0.1790(24) (12) (12) (18) 1. (1) (2) * (3) (4) (3)(4) + (4) 3. (5) 4. 89
27 l n Y / H b 1 b 2 b (1)
28 ( 1 ) ( 2 ) ( 3 ) * * * l * * ((1)/(3)) 4 91
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地域総合研究第40巻第1号
* abstract This paper attempts to show a method to estimate joint distribution for income and age with copula function. Further, we estimate the joint distribution from National Survey of Family Income
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