B.2 EXCEL B.3 tara B.4 CSV
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1 Numeric Recipes for Econometrics(0) SHIMURA Masato AR A 38 B EXCEL 39 B
2 B.2 EXCEL B.3 tara B.4 CSV (AR) y X X X X 1 X 2 X 3 X n,.y (y Example (i js) DN11 * Stich(,.) (,) 6 33 EX0=: 1 2 3,4 5 6,: ijs =: EXCEL CSV *2 EXCEL CSV APPENDIX ( ) (GDP) () () () *1 = (equal) *2 Camma Separared Value 2
3 *3 ( ) CSV *4 require files csv plot ] DN10=. ".@> readcsv /data/excel/stat_j/csv/ban_1.csv /data/excel/stat_j/csv/ EXCEL CSV =. (L:0) DN10 = ;( 1) ( ;( 2)) = ".@>. J 1 2 (J J, 0 ( 1) *3 numeric recipe data.ijs *4 CSV Camma Separated Value () EXCEL DB CSV 3
4 ( Take { Take f irst {. 0{ 1 DN11 Tale last {: {: 1 DN11 Drop f irst }. }. 1 DN11 Drop last }: } : 1 DN11 J n * 5 f unction name U sage 0 puc pickup column rec remove column puc set pickup with set 1 puc1 pickup column rec1 remove column puc set1 pickup with set puc=:pick_column=: [ {"1 ] puc1=:pick_column=: (>:@[) {"1 ] rec=:remove_column=: 4 : (I.-.(i.{:@$ y ) e. x ) puc y NB. remove_raw rer=: remove_raw=: 4 : (I.-.(i. # y ) e. x ) { y Example ] a=.?. 7 4 $ puc a rec a *5 0, 1, 2, 3 0 1, 2,
5 y X y 2 2 1,.X 0,.X 1,.X 2,.X n ( 1 ) y %. 1,.X 1,.X,.y y reg_ols=: %. 1&,.@] y, X J x y type 1 type 2 y is 0, x is 1 (0 puc a) reg_ols 1 puc a f = x y is 0, x is ( ) (0 puc a) reg_ols 0 rec a _ _ y = x x x 2 y is 0 x is 3 (0;3) puc_set a x y 3 0 puc a 8 6 x y regx (0;3) puc_set a _ y = x y is 0 x is 1 3 (0; 1 3) puc_set a x0 x1 y 5
6 regx (0;1 3) puc_set a _ f = x x *6 EPS EMF J sin title sin plot _5 5 ; 1&o. NB. sin from _5 to 5 pd eps /temp/sin0.eps NB. save by eps 5 5 plot (/temp ) J Grammar *6 J 6
7 ". format ": >open Box < Box require readcsv csv require files csv plot pd plot driver eps 7
8 Matrix divide (AR) 3 %. matrix Divide K.E.Iverson *7, Ordinaly Least regx=: 3 : ({:"1 y ) %. 1,.}:"1 y Square OLS Polynomial poly1=:4 : y %. (>:i. # y )ˆ/i. >: x Auto Regression AR ar0=:4 : (x }.tmp) %..("1)}: >x <\ tmp=:y -(+/%#)y OLS y 1 1 x 11 y 1 1 x 11 x 21 x k1 y = y 2 y 3 y n, 1 x 12 1 x x 1n y = y 2 y 3 y n, 1 x 12 x 22 x k2 1 x 13 x 23 x k x 1n x 2n x kn (X X)ˆβ = X y *7 APL /. 8
9 ˆβ = (X X) 1 X y (X X) 1 X y = X y X X = y X X 1 Working Example DN11 X cm Y (%) y 1,.X DN11 K.E.Iverson matrix divide (%.) 9
10 1.2.3 X,.Y X 1 y X Y 1,.X %. DN11 X Y ,.0 puc DN y %. 1,.X (1 puc DN11) %. 1,. 0 puc DN11 _ reg0 DN11 _ y = x *8 Script reg0 reg0=:3 : 0 NB. select trend d ata or multi data if. 1= +/ * $ y do. reg_t y elseif. do. regx y end. ) reg_t=:3 : y %. 1,. >: i. # y regx=:3 : ({:"1 y ) %. 1,.}:"1 y *8 X Y reg_t reg0 DN11 regx 10
11 X 1 (X X) 1 X y = X y X X = y X %. ({:"1 DN11) %. {."1 DN (1 puc DN11) %. 0 puc DN y = x reg exam ad reg0 reg_exam_ad *9 reg0 reg_exam_ad DN f= _ *9 ( ) J 11
12 corr=: AIC: AIC DW= / t=: _ t line f it reg0 linefit_reg0 DN11 pd eps /temp/reg_0.eps NB. Save J 1 : 0 i. i i: 3 _3 _2 _ >: 1. <: 1 %. matrix divide = 12
13 +/ +/
14 1.3 y t k y = C 00 + C 01 t + + c 0k t k + ɛ S 0 S 1 S k S 1 S 2 S k+1 S 2 S 3 S k S K S K+1 S 2k c 0 c 1 c 2 c K T 1 T 2 T 3 T k * 10 Example 2 y = x x x 3 3 poly0 DN _ ( ) ( )4 4 linefit_poly0 DN12 *10 14
15 10 3 poly0 10?. 20 _ _ f x = x x x 3 X,.a = 10?. 20 X X 1 (>:i. # a),.a (1 (>:i. # a)ˆ/ i. >:
16 AIC AIC k AIC J ˆ?,?. # n $ 1.4 AR AR (AR Auto Regressive Model) M AR Autoregressive Model S 11 S 12 S 1k S 12 S 22 S 2k S 13 S 23 S 3k S 1K S 2K S kk b 1 b 2 b 3 b K = T 1 T 2 T 3 T k Yull Walker Burk Householder *11 (DN12) 3 *11 3 Burk Yull Walker householder 16
17 1. x t 1, x t 2, x t 3,, x t n (X) 2. (y) y 3. X X NR, y 3 y, x t 0, x t 1, x t 2, x t (3}.DN12),.}:."1 >3<\DN12 Y x t 1 x t 2 x t cut cut cut cut ini f ix(\) X Box( ) in f ix(\) Open( ) x t 1, x t 2, x t 3 Rotate(. 1) Y 3 1. "1>3<\ >:i (%.) 17
18 1.4.2 AIC Mll = n k n (logq k/(n k)) AIC = 2 MLL + 2 k = (n k) (logq k /(n k)) + 2 k AR AIC k 4 exam_ar0 DN mean=6.904 corr= AIC= exam_ar0 DN mean=6.904 corr= AIC= exam_ar0 DN mean=6.904 corr= AIC= ar0 DN _ t t t t 4 4 linefit_ar DN12 pd eps \temp\ar_0.eps 18
19 12 native estim reg0 reg exam ad reg0 reg exam ad n estim reg0 line f it reg0 estim reg0 n linefit reg0 n poly0 poly exam linefit poly0 ar0 exam ar0 4 poly exam n 4 linefit poly0 n m ar0 n m exam ar0 n 19
20 ]a=: >: i Script Example 1 n n X i am=: +/ % # i=1 am2=: # % +/ 5.5 am a n Π n i=1 X i gm=: # %: */ n ni=1 1 X i hm=: am &.(%"_) gm a */ 0 hm a
21 common mean m x m x m n n cm=:[: {.(am,gm)ˆ:_ cm a ( ) 1 f 1 ni=1 f x i n km km km km km km km hm % +/ 1r30 1r40 1r = (( y t y t 1 ) 4 1) qtr_grow NB % Script qtr_grow=: 3 : 100 * <: ˆ&4 %/. y NB. e.g. u NB. exchange rate of growth from quarter to year 21
22 (rotate.) %/ ˆ4 1 (<: 1 ) <: ˆ&4 %/ ( times) 100 * <: ˆ&4 %/ % n xt+n x t Script grow_ave=: 4 : 100 * <: (x %: %/. y) %/ NB. GDP 1995/ %: %/ NB. GDP 1995/
23 * 5 %: %/ NB. GDP 1995/ Working Example 5 grow_ave NB. GDP 1995/ % 10 grow_ave NB. GDP 1990/ (1.39%) DN gm DN Working Example DN year % gm DN NB. 8.67% per year J 23
24 i. 0 >: 1 * % *: square 2 %: square root n {. From _ in f inity child "1 Rank 1 ˆ: power &. under y. Rotate / Insert ( ) <: Decriment 1 & ( ) r 1r
25 = y t y 00 3 Laspiress pt q 0 p0 q 0 Parshe pt q t p0 q t Fischer pt q 0 p0 q 0 pt q t p0 q 0 DN22 A B NB NB NB NB DN22=:( , ) ; , ( ) lsp_chain0 DN NB par_chain0 DN22 25
26 fis_chain0 DN Working Example 1 DN23=: , , , , ,: DN23=: ( ; )<;.1 DN23 DN NB. Cabbages NB. Spinachs NB. Napa NB. Leek NB. Lettuce NB. Broccoli lsp DN23 Las: Par: Fis: Script lsp=: 3 : 0 NB. Calc Laspi Parshe Fischer P0 Q0 P1 Q1 =: {;("2),. : L:0 y las=.(+/ P1 * Q0)% +/ P0 * Q0 par=.(+/p1 * Q1)% +/ P0 * Q1 fis=.%:(las * par) Las: Par: Fis:,: 9j3 ":100 *(las, par,fis ) 26
27 ) Laspeyres Étinne Laspeyres( ) Lass-pey-ress Wikipedia J n { take Las character 12j5 ": f ormat (12 5 ) 2.4 x x 1 (x x) 2 n x cm y (%) DN stand DN24 _ _ _ _ _ _ _
28 1 0 key fruits water plot : stand DN24 pd eps \temp\kanaya_02.eps ( ) Script stand=: dev % "1 sd dev=: -"1(+/ % #) sd=. %:@var var=: # % ([:+/[: *: dev) J *: square 2 (ˆ2 ) %: square root 2 ( ) -"1(+/%#) x x [: Cap 28
29 2.4.2 x x -(+/%#) ( ) 2.5 e log ln J ˆ. ˆ.100 ˆ ˆ e y = x logx = y 1x J 1x1 e ˆ. DN
30 J ˆ. naturel log 10 ˆ. 100 is 2 ˆ e n ˆ is 100 1x1 e e 2x1 1x2 2.6 x = x x = x1 2 + x x2 n ( ) 2 1 (Euclid) norm=: [: %: [: +/ *: The length(or norm)of v is the nonnegative scalar v x = v v = x1 2 + x x2 n v 2 = v v x y = (x 1 y 1 ) 2 + (x 2 y 2 ) 2 (x n y n ) 2 PQ Example euc_norm 1 _ _ v = v = ( ) = 9u = 1 v v Script norm=: [: %: [: +/ *: euc_norm=: 3 : y. % norm y. Coffee Brake John Napier( ) 1614 e 30
31 x = 1 n n i=1 X i (x x) 2 ss=: [: +/ (*:@dev) mean=: +/ % # NB. am dev=: - mean var=:ss%# Variance (x x) 2 n Standard deviation (x x) 2 sd x n sd=: %:&(ss%#) vr=: sd % mean cov=: # % ([: +/ [: */"1 dev) 1 (x x)(y ȳ) N dev=: -"1(+/ % #) cov=:# % ([: +/ [:*/ "1 (-"1(+/ % #))) ( ) 31
32 2.7.2 V(X 1 + X X n ) = V = n V(X i + Cov(X i, X j ) i=1 S xx S xy S xz S yx S yy S yz S zx S zy S zz i j x y x1 y1 x2 y2 x3 y3 x4 C = y4 t XX N x 1 x y 1 ȳ = 1 x 1 x x 2 x... x n x x 2 x y 2 ȳ N y 1 ȳ y 2 ȳ... y n ȳ x 3 x y 3 ȳ x n x y n ȳ ( ) ( 1 (xn x)(x n x) (x n x)(y n ȳ) x = N (y n ȳ)(x n x) (y n ȳ)(y n ȳ) ) 32
33 2.7.3 Worked Example DN25 NB. (1) dev2 DN25 NB. (2) _10 _10 _10 _10 _10 _5 0 _5 _5 _5 _5 0 _5 0 0 _ _ _
34 ( : dev2 DN25) +/. * (dev2 DN25) NB. (3) n n = 10 (( : dev2 DN25) +/. * (dev2 DN25)) % # DN25 NB. (4) vartable DN Script vartable=:# % :@dev2 +/.* dev2 J +/. * : Transpose 2.8 R = 1 r xy r xz r yx 1 r yz r zx r zy 1 X, Y ρ XY = Cov(X, Y) V(X) V(Y) ρ xy = (x, y) x y Working Example cortable DN25 34
35 Script cortable=: 3 : 0 ss=. [: +/ [: *: dev2 sd=. %:&(ss%#) stand=. dev2@] %"1 sd@] cortable=. #@] % ( :@stand@] +/. * stand@]) cortable y ) Atop -"1(+/%#) -"1 is hook 2.9,,,, r i j R = [ r i j ] R R 1 r i j r i j.o = ri j r ii r j j X 1 X 2 R = [ r i j ] R R 1 r i j r i j.o = ri j r ii r j j 35
36 5 DN cortable DN pcor_table cortable DN26 1 _ _ stand stand n mean dev var sd cov 36
37 vartable vartable n cortable cortable n pcor table pcor table cortable n am am2 gm hm am i.10 gm i.10 hm i.10 qtr grow grow ave qtr grow grow ave lsp lsp n lsp chain0 par chain0 fis chain0 norm norm n 37
38 A ] a=. i from ( _1 { a _1 {a NB. rank is default from ( 0 2 _1 {"1 a ( 1) 0 2 _1 {"1 a take ({.) 2{."1 a
39 B EXCEL EXCEL Libre CALC biff-8 EXCEL2003 EXCEL2007 biff-12 biff XML ) EXCEL2003 (2007 OK,2010?) tara Libre-Office () B.1 tara Net J Run/Package Manager tables/excel,tables/tara DL Net J CDROM,Net J602 copy B.2 EXCEL ( B.3 tara require files B.3.1 tara.ijs tara.ijs j602/addons/tables/tara/tara.ijs tutorial (tara.ijt) addons/tables/tara/tara.ijt. dir =. /data/sna/esri/principal/2010/ a=.readexcel dir, shouhi_test.xls tara Open BOX ;("1) 9}. 2 4 {"1 a Sheet. 39
40 Sheet1 readexcel dir, test_calc.xls B.3.2 *12 EXCEL bi=. conew biffbook writenumber bi 0 0 ;i writenumber bi 0 0 ;a1 NB. (example) a1=.? $ 100 save bi /temp/testtara.xls underbar 2 ) a1=. i a1 writexlsheets /temp/tararest.xls *12 tara jmacros.xls J602 csv 40
41 B.4 CSV B.4.1 CSV save CSV Comma Separated Values EXCEL ( copy EXCEL csv Example CSV index shouhi test.csv save B.4.2 CSV J require files csv dir=: c:/data/sna/esri/principal/2010/ ] a=. readcsv dir, shouhi_test.csv ] a=. ".@> readcsv dir, shouhi_test.csv ] a=. ;("1) ".(L:0) a 41
42 References 2000 J 1996 [] 1985 Miscellance J602 is download available (No charge) Scripts are accessible 42
R/S.5.72 (LongTerm Strage 1965) NASA (?. 2? (-:2)> 2?.2 NB. -: is half
SHIMURA Masato JCD2773@nifty.ne.jp 29 6 19 1 R/S 1 2 9 3 References 22 C.Reiter 5 1 R/S 1.1 Harold Edwin Hurst 188-1978 England) Leicester, Oxford 3 196 Sir Henry Lyons ( 1915 1946 Hurst Black Simaika
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![1 1.1 p(x n+1 x n, x n 1, x n 2, ) = p(x n+1 x n ) (x n ) (x n+1 ) * (I Q) 1 ( 1 Q 1 Q n 0(n ) I + Q + Q 2 + = (I Q) ] q q +/. * q](/thumbs/93/113048245.jpg "1 1.1 p(x n+1 x n, x n 1, x n 2, ) = p(x n+1 x n ) (x n ) (x n+1 ) * (I Q) 1 ( 1 Q 1 Q n 0(n ) I + Q + Q 2 + = (I Q) ] q q +/. * q")
Masato Shimura JCD02773@nifty.ne.jp 2008 7 23 1 2 1.1....................................... 2 1.2..................................... 2 2 3 2.1 Example...................................... 3 2.2 Script...........................................
80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x
80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = n λ x i e λ x i! = λ n x i e nλ n x i! n n log l(λ) = log(λ) x i nλ log( x i!) log l(λ) λ = 1 λ n x i n =
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1 SHIMURA Masato 2010 9 27 1 1 2 CF 6 3 10 *1 irr irr irr(inner rate of return)function is able to written only few lines,and it is very powerful and useful for simulate unprofitable business model. 1
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/ WIN [ ] Masato SHIMURA JCD2773@nifty.ne.jp Last update 25 4 23 1 J 2 1.1....................................... 2 2 D 2 2.1 numeric trig................................... 6 3 6 3.1 X;Y....................................
第11回：線形回帰モデルのOLS推定
11 OLS 2018 7 13 1 / 45 1. 2. 3. 2 / 45 n 2 ((y 1, x 1 ), (y 2, x 2 ),, (y n, x n )) linear regression model y i = β 0 + β 1 x i + u i, E(u i x i ) = 0, E(u i u j x i ) = 0 (i j), V(u i x i ) = σ 2, i
6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4
35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
AR(1) y t = φy t 1 + ɛ t, ɛ t N(0, σ 2 ) 1. Mean of y t given y t 1, y t 2, E(y t y t 1, y t 2, ) = φy t 1 2. Variance of y t given y t 1, y t
87 6.1 AR(1) y t = φy t 1 + ɛ t, ɛ t N(0, σ 2 ) 1. Mean of y t given y t 1, y t 2, E(y t y t 1, y t 2, ) = φy t 1 2. Variance of y t given y t 1, y t 2, V(y t y t 1, y t 2, ) = σ 2 3. Thus, y t y t 1,
.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(
06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,
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renshumondai-kaito.dvi
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応力とひずみ.ppt
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Files Masato SHIMURA JCD02773@nifty.ne.jp 2004/12/11 last update 2005/02/05 1 2 1.1 WINDOWS................................. 2 2 2 2.1 EXCEL OLE................................ 2 2.2 CSV..................................
s = 1.15 (s = 1.07), R = 0.786, R = 0.679, DW =.03 5 Y = 0.3 (0.095) (.708) X, R = 0.786, R = 0.679, s = 1.07, DW =.03, t û Y = 0.3 (3.163) + 0
7 DW 7.1 DW u 1, u,, u (DW ) u u 1 = u 1, u,, u + + + - - - - + + - - - + + u 1, u,, u + - + - + - + - + u 1, u,, u u 1, u,, u u +1 = u 1, u,, u Y = α + βx + u, u = ρu 1 + ɛ, H 0 : ρ = 0, H 1 : ρ 0 ɛ 1,
最小2乗法
2 2012 4 ( ) 2 2012 4 1 / 42 X Y Y = f (X ; Z) linear regression model X Y slope X 1 Y (X, Y ) 1 (X, Y ) ( ) 2 2012 4 2 / 42 1 β = β = β (4.2) = β 0 + β (4.3) ( ) 2 2012 4 3 / 42 = β 0 + β + (4.4) ( )
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73 74 ( u w + bw) d = Ɣ t tw dɣ u = N u + N u + N 3 u 3 + N 4 u 4 + [K ] {u = {F 75 u δu L σ (L) σ dx σ + dσ x δu b δu + d(δu) ALW W = L b δu dv + Aσ (L)δu(L) δu = (= ) W = A L b δu dx + Aσ (L)δu(L) Aσ
数学の基礎訓練I
I 9 6 13 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 3 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............
, = = 7 6 = 42, =
http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8
第13回：交差項を含む回帰・弾力性の推定
13 2018 7 27 1 / 31 1. 2. 2 / 31 y i = β 0 + β X x i + β Z z i + β XZ x i z i + u i, E(u i x i, z i ) = 0, E(u i u j x i, z i ) = 0 (i j), V(u i x i, z i ) = σ 2, i = 1, 2,, n x i z i 1 3 / 31 y i = β
40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x,
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II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
![II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2](/thumbs/101/149159646.jpg "II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2")
II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh
96 7 1m =2 10 7 N 1A 7.1 7.2 a C (1) I (2) A C I A A a A a A A a C C C 7.2: C A C A = = µ 0 2π (1) A C 7.2 AC C A 3 3 µ0 I 2 = 2πa. (2) A C C 7.2 A A
7 Lorentz 7.1 Ampère I 1 I 2 I 2 I 1 L I 1 I 2 21 12 L r 21 = 12 = µ 0 2π I 1 I 2 r L. (7.1) 7.1 µ 0 =4π 10 7 N A 2 (7.2) magnetic permiability I 1 I 2 I 1 I 2 12 21 12 21 7.1: 1m 95 96 7 1m =2 10 7 N
,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.
9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,
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5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )
5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y
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液晶の物理１：連続体理論（弾性，粘性）
The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers
講義のーと : データ解析のための統計モデリング. 第５回
Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
2 1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a 2 + b 2 α (norm) N(α) = a 2 + b 2 = αα = α 2 α (spure) (trace) 1 1. a R aα =
1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a + b α (norm) N(α) = a + b = αα = α α (spure) (trace) 1 1. a R aα = aα. α = α 3. α + β = α + β 4. αβ = αβ 5. β 0 6. α = α ( ) α = α
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chap10.dvi
. q {y j } I( ( L y j =Δy j = u j = C l ε j l = C(L ε j, {ε j } i.i.d.(,i q ( l= y O p ( {u j } q {C l } A l C l
ＪＭＰ V4 による生存時間分析
V4 1 SAS 2000.11.18 4 ( ) (Survival Time) 1 (Event) Start of Study Start of Observation Died Died Died Lost End Time Censor Died Died Censor Died Time Start of Study End Start of Observation Censor
n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)
D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y