1
10:30 12:00 P.G. vs vs vs 2
LOGIT PROBIT TOBIT mean median mode CV 3
4
5
0.5 1000 6
45 7
P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B A)P(A) P(A B) ------------------------------------- P(B A)P(A) P(B A c )P(A c ) 8
9
10
P( ) P( ) 1- X P( X=x ) C x p x q n-x B(n,p) 11
X n x λ p(x) C x λs n x λs n n-x p(x) λ x exp λ x! X 0,1, 12
x a<x<b a b 1/ ba E(x)= 1/ b-a ab xdx =(a+b)/2 V(x)=(b-a) 2 /12 13
normal distribution N µ 0 1 N 0, 1 µ 14
N 0 1 µ=0 σ 2 =1 - s + s µ 68.2% 95.4% 15
µ=0 σ 2 =0.5 N (0, 1) N (0, 2) N (0, 0.5) σ 2 =1 σ 2 =2 16
µ = -2 µ = 0 µ = 2 N (-2, 1) N (0, 1) N (2, 1) σ 2 =1 17
µ µ X,Y 18
19
X µ σ 2 X n {X 1 X 2 X n } µ /n 20
2 i 1, 2,., m i µ 21
3 Z 22
4 X n {X1 X2,, Xn} X µ c 23
5 X n {X1 X2,, Xn} c 24
6 n {X1 X2,, Xn} i 1, 2, n µ n 25
7 n {X1 X2,, Xn} n 1 2 26
χ 2 t χ 2 χ 2 27
2 Z1 Zk k k 28
χ 2 W W Z1 Z1 1 W k W Z Z 2 k 2 E(z 4 =3 V W 2k 2 Xi µ k 29
χ 2 3 2 2 5 1 10 2 2 4 6 8 10 12 16 30
t Z W k Z W k t k t t t 1 2 3 31
t 0 k/(k 2) 1 1 t 32
Z P c P Z c 33
F V m W k V W V W m k F F F F k/(k 2) k 3 k 1 34
F 0.8 2.20 0.6 5.20 0.4 0.2 1 2 3 4 5 35
estimator vs estimate vs vs 36
µ 12 76, 63, 83, 86, 53, 71 95% Z= -1.96 0 1.96 = 64.2 81.8 µ σ 2 /n= 144/6 24 Z 95% P( 1.96 Z 1.96 ) 0.95 72 µ 64.2 µ 81.8 37
(unbiasness) consistency efficiency sufficiency 38
moment method (maximum likelyhood method) 39
(alternative) hypothesis (null hypothesis) p p 0 test statistics) 10% 25 25 40
critical value) α β 41
1%,5%,10% 42
25 P: P 0 : H 0 : P P 0 Ha: P P 0 H 0 : P P 0 H 0 : P P 0 43
3.1kg 0.2kg 25 3.0 3.1kg 3.1kg 0.2/5 0.04 44
α 0.05 β=0.198 H a :µ=3.1 H 0 :µ=3.1 α β Z=-2.5( =3) Z=0 ( =3.1) Z=-1.65( =3.034) 45
46
1986 17 171.5cm 158.5cm 450 1949 17 161.2cm 152.2cm µ 1986 5.75cm 5.07cm 37 µ 161.2 µ 152.2 µ 161.2 µ 152.2 47
C 48
n-1 49
1200 100 µ=1200 µ 1200 1230 120 n 100 1% z 0 =2.33 X 1200+(120/10)2.33=1228 1% P 0.01 α 0 ξ 100α µ 100α ξ α µ 100(1- α)% µ 0 µ 0 50
51
1) 2) n 1 +n 2-2 t 3) σ 12 σ 22 12 S 22 52
3) 6.3 6.4 53
100 α/2 Z0 25 100 α/2 Z 0 b=1.65, p=1/6-1.65{1/6(1-1/6)/25} 0.5 =0.044, 25 1.1 0 1 54
55
2 X,Y ρ n-2 T r=-0.655 T 3.0 n=12 5% -1.782 4 56
f(x,θ) L 0 L a La 0 λ 6.1 X X 1 X n θ θ 1 θ k H 0 θ 1 =c 1 θ c n -2log(λ) χ 2 χ2 57
χ χ E = n x x TSS = 58
59
60
61
62
63
64
65
correlation coefficient 2 66
20 ( ) = α + β ( ) + 67
( ) (kg) 68
69
y y j y k µ k µ j x 70
y y j µ j y k µ k U i (0,σ 2 ) (i=j,k) x 71
72
73
74
75
76
(1),(2) a b n 77
78
79
80
81
82
83
0 84 2.5
0 2.5 85
86
1.440 20 87
88
---- ---- DW DW 2(1 r) DW 2.190422 89
DW dl du dw<dl du<dw<4-du 4-dL<dw DL<dw<dU 4-dU<dw<4-dL 90
DW 10 h<-645-1.65<h<1.645 1.645<h 1-nv 0 e j e j-1 e j-1 91
1% 1.441 95% 0.927 1.955 0.65 DW 2.19 92
93
94
95
1.037 95 0.819 1.256 96
1% P DW 97
98
99
100
FI* FI* FI* β 1 β 2 X i ei FI FI* FI
FI* FI FI Pi Pr FI= Pr FI* Pr ε i β 1 β 2 X i Pr ε i β 1 β 2 X i (1) ε i (1) P i Pr ε i β 1 β 2 X i Φ β 1 β 2 X i
β 1 β 2 Δ β 1 β 2 X i
2 Censored odel Truncated model FI* FI i * β 1 β 2 X i i FI FI*
FI* FI* 0
FDIB z- - -1.195-1.74 0.08 SB 0.022 17.2 0.00 ET 1.319 3.47 0.00 APCC -2.438-2.25 0.02 NAFTA 0.733 1.067 0.28 EU -2.142-0.838 0.40 _89 1980 0.077 0.195 0.84 22.3 AIC=-0.872 33 NAFTA EU 1980
FDIB z- - C -30.837-2.78 0.00 SB 0.030 0.15 0.87 ET 8.608 1.55 0.11 APCC -18.149-1.90 0.05-122.9 AIC=1.96 130
FDIB z- - C -0.052-0.31 0.75 SB -0.008-0.17 0.86 ET 1.159 4.99 0.00 APCC -0.231-1.55 0.11 _89 ) 0.232 1.39 0.16 35.6 AIC=-2.12 28 1980
4 FDIB z- - C 0.338 2.21 0.02 SB 0.038 1.23 0.21 ET -0.388-0.64 0.52 APCC -0.259-1.38 0.16 _89(80 ) 0.298 1.22 0.21 8.85 AIC=-0.38 15 1980
RDSA FDI [FDI] [RDSA]=17.44 [RDSA] LSALE FDI [FDI] ( ) [LSALE]=6.214 [LSALE]
33 4 p149 183 1979 10
< > < >
Rxy(τ τ
Dxy(θj Px (θj X Y X(t) Y(t) πθj τ θj X(t) Y(t) τ θj X(t) Y(t)
MBP kg 1962 1 1976 12 180 AOP kg 1962 1 1976 12 180 STN 1962 1 1976 12 180
χα22(v) α% α α χ2 P(θj V V
ii iii
50ha X 1 ha X 2 ha ha 1ha 100 ha 50 ha 100 3000 ha 80 ha 100 ha X 1 + X 2 50 X 1 + X 2 100 50X 1 + 100X 2 3000 80X 1 + 100X 2 Z 122
XX2 2 X 2 =0.8X 1 +0.01Z 123
(i) x 1,x 2,x 3,x 4 S y 1,y 2,y 3 y 1 50 y 2 =100 y 3 =3000 (ii) y 1,y 2,y 3 0 (iii)z j -C j S 0 (i) Z j -C j (ii)s R 2 (iii) (iv) (iii) 2 (v) Z j -C j Zj Cj Z j C j 2 Z j -C j 3 Z j -C j R Z j -C j S y2=20 20 =40 40 x2=10 10ha Z 124 j - C j =4200 4200
y2 125
X1 + X2 10 11 20 X1 + 40 X2 360 45 X1 + 22.5 X2 360 Z X1 + X2 126
127
128