NB. ======================================== NB. ================================ NB. Stadt 0 NB. ================================= abs=:| atn=:_3&o. cint=:<.@+&0.5 cos=:2&o. exp=:^@] int=:<.@] left=:{.@] log=:^.@] right=:{.&.|. sgn=:*@] sin=:1&o. sqrt=:%:@] tan=:3&o. mean=:+/%# mean DATA mav=:+/\%[ rank=:$&$ D=:>:i.4 5 mean1=:3 : '(+/%#)y ' mvsd=:3 : 0 m=:(+/%#)y ss=:+/@(*:@-"1&m)y sd=:%:V0=:ss(%#)y m,V0,:sd ) mave=:4 :' (x+/\y )%x' gcd=:3 : 0 +./y : x+.y ) NB. ============================================== NB. Satdt 1 NB. ============================================= max=:3 : 0 >./y : x>.y ) min=:3 : 0 <./y : x<.y ) order=:/:~ rng=:>./ - <./ rngq=:3 : 0 r=:a,b,b+a=:<.-:b=:<.0.5+-:#y ({:-{.)-:+/"1(r{Y0),.(<:r){Y0=:/:~y ) mean=:+/ % # meang=:# %: */ NB. meanh=:mean&.% NB. * * * * * * * * * * * * * * * * NB. ss=:+/&*:&(- mean) ss=: [: +/ *:&(- mean) sd=:%:&(ss % #) mesd=:mean,sd var=:ss % # corro=:3 : 0 m=:+/(k=:(+/%#)&>y )*w=:N0%+/N0=:#&>y V0=:(((+/"1*:(>y )-k)%N0),:*:k-m)+/ . * w w=:'within variance :',8j2":{.V0 b=:'between variance :',8j2":bv=:}.V0 t=:'total variance :',8j2":V0=:+/V0 w,b,t,:'correration ratio :',8j2":bv%V0 ) mav=:+/\ % [ smexp=:4 : 0 s=:{.Y0=:y while. 1<#Y0 do. s=:s,(x*{:s)+(1-x)*{.Y0=:}.Y0 end. ) stand=:(] - mean@])%sd@] cor=:+/@([ *&stand ]) % #@] reg=:[%.1&(,"0)@] cly=:>.@(] % [) acum=:~. ,"0 (+/"1@=) table=:acum@order@cly grf=:3 : 0 (,.~.y );{&' *'Y0>:/>:i.>./Y0=:+/"1@=y ) NB. ==================================== NB. Stadt 2 NB. ==================================== rnd=:3 : 0 ?y $100 : y ?x ) dice=:>:@?@($&6)@] acum=:~. ,"0 (+/"1@=) card=:3 : 0 b=:4+13|a=:/:~y ?52 {&'CDHS23456789TJQKA'(<.a%13),.b ) cardb=:3 : 0 a=:(b=:>.a%13),.5+13|a=:>:/:~y ?52 <"1 {&' CDHSA23456789TJQK'((>:i.4)=/b)#a ) bic=:i.&>: ! ] pascal=:":@bic"0@i. NB. ************ binom=:4 : '(k!x)*(y ^k)*(1-y )^|.k=:i.1+x ' bden=:4 : ' (>:<./M0,x){.(M0{.p),+/(M0=:+/p>1e_3)}.p=:x binom y ' bgf=:4 : 0 (,.i.#a);{&' *'a>:/>:i.>./a=:<.0.5+80*x bden y ) bmev=:[*]*1:,1:-] pden=:3 : 0 p=:(^-y )*(y ^k)%!k=:i.5+>.+:y p,1-+/p=:(+/p>1e_3){.p ) NB. ************* ndens=:3 : '(^--:*:y )%%:o.2' nden=:4 : '(ndens(y -{.x )%s)%s=:%:{:x ' ndfs=:3 : '(-:h*(ndens 0)+ndens y )+h*+/ndens(>:i.249)*h=:y %250' ndf1=:0.5&+@(* * ndfs) ndf2=:0&>.@-~&(* * ndfs) NB.ndf=:ndf1 :ndf2 NB. *************** << 2.15>> *************** nrnd=:3 : '+/?(12,y )$6' nrne=:3 : '<.0.5+(nrnd y )%5' acum=:~. ,"0 (+/"1@=) order=:/:~ NB. ============================== NB. Stadt 3 NB. ============================= NB. *************** << 3.3 >> *************** civl=:4 : '(x +2+(-,+)+:%:(x +(y -x )*x +1)%y )%y +4' civld=:4 : 0 w=:X0*(M0-X0=:{.x )%(M0=:{:x )^3 w=:+:%:w+Y0*(N0-Y0=:{.y )%(N0=:{:y )^3 |.((X0%M0)-Y0%N0)+w,-w ) nrnd=:3 : '+/?(12,y )$6' nrne=:3 : '<.0.5+(nrnd y )%5' estim=:3 : 0 M0=:(+/d=:(p=:?10)+nrne N0)%N0=:y w=:+:(-s),s=:%:(+/*:d-M0)%N0 e=:'point estimation :',6j2":M0 c=:'confidence interval :',6j2":M0+w e,c,:'population mean :',3":p+6 ) NB. *************** << 3.6 >> *************** estimd=:4 : 0 M0=:(+/X0=:(p=:?5)+nrne x )%x d=:M0-N0=:(+/Y0=:(q=:?5)+nrne y )%y V0=:(+/*:X0-M0),+/*:Y0-N0 w=:+:(-s),s=:%:+/V0%*:(x ),y e=:'sample mean diff. :',6j2":d c=:'confidence interval :',6j2":d+w e,c,:'mean difference :',3":p-q ) NB. *************** << 3.8 >> *************** chigf=:3 : '(+/*:y -e)%e=:(+/y )%#y ' dice=:>:@?@($&6)@] diceb=:3 : '/:~6<.>:?y $7' NB. *************** << 3.9 >> *************** chitr=:4 : ' (+/y **:p-q)%q*1-q=:(+/%#)p=:x %y ' NB. *************** << 3.10>> *************** testgf=:4 : ' +/(*:y -t)%t=:x *+/y ' NB. *************** << 3.11>> *************** chic=:3 : '(+/,y )*(*:-/ . *y )%*/(+/"1 y ),+/y ' testc=:3 : 0 p=:,(+/"1 y )*/+/y +/(*:p-(*+/),y )%p*+/,y ) NB. =============================== NB. Stadt 4 NB. =============================== NB. *************** << 4.4 >> *************** kli=:+/@([*^.@([%])) binom=:4 : '(k!x )*(y ^k)*(1-y )^|.k=:i.1+x ' NB. *************** << 4.5 >> *************** klin=:4 : '-:<:(^.V0%U0)+((U0=:}.x )+*:({.x )-{.y )%V0=:}.y ' NB. *************** << 4.8 >> *************** ratio=:4 : 0 A0=:-+:+/((k=:{.y ),--/y )*^.(x ),1-x A1=:2-+:(+/(*^.)k,N0-k)-(*^.)N0=:}.y A0=:'theoretical model :',8j2":A0 A0,:'empirical model :',8j2":A1 ) NB. *************** << 4.9 >> *************** cont=:3 : 0 C=:(N0=:+/,y )*(*:-/ .*y )%*/d=:(+/"1 y ),+/y A2=:4-+:(+/(*^.)d)-+:(*^.)N0 A3=:6-+:(+/(*^.),y )-(*^.)N0 A2=:'AIC(indep) :',8j2":A2 A3=:'AIC(dep) :',8j2":A3 ('chi-square :',8j2":C),A2,:A3 ) NB. *************** << 4.11>> *************** aic1=:4 : 0 M0=:(+/z)%N0=:$z=:(x ),y V0=:((+/*:z)%N0)-*:M0 (4+N0*1+^.(o.2)*V0),M0,V0 ) aic2=:4 : 0 M0=:((+/x ),+/y )%N0=:($x ),$y V0=:((+/*:(x ),y )-+/N0**:M0)%+/N0 (6+(+/N0)*1+^.(o.2)*V0),M0,V0 ) NB. *************** << 4.12>> *************** pit=:3 : 0 pol=:+/@([*]^i.@(#@[)) dif=:}.@(]*i.@(#@])) X0;Y0-(X0 pol Y0)%(dif X0=:>{.y )pol Y0=:>{:y ) pnm=:>@{:@(pit^:10@([;])) aic3=:4 : 0 m1=:{.M0=:x (,.&((+/%#)@(],.*:@])))y A=:+/(1+|.a=:(]%+/)N0=:x ,&$y )*m1 B=:(+:*/m1)++/(|.a)*m2=:{:M0 (C=:+/a*m1*|.m2);V0=:m2-*:m1 M0=:((-C),B,(-A),1)pnm(+/m1*|.V0)%+/V0 (6++/N0*1+^.V0*o.2),M0,V0=:V0+*:m1-M0 ) aic4=:4 : 0 M0=:((+/x ),+/y ) % N0=:($x ),$y V0=:(((+/*:x ),+/*:y )%N0)-*:M0 (8+(+/N0)*1+^.(o.2)**/V0),M0,V0 ) NB. ======================================== NB. Stadt 5 NB. ======================================== NB. *************** << 5.1 >> *************** decomp1=:3 : 0 V0=:(y )-M0=.(k=:$y )$(+/%#),y wv=:V0-bv=. |:(|.k)$(+/%#)|:V0 d=:y ;'=';M0;'+';V0 2 1 5 $ d,V0;'=';bv;'+';wv ) NB. *************** << 5.2 >> *************** av1=:3 : 0 s=:|:y -(+/%#),y sb=:+/*:,(|.k=:$y )$(+/%#)s sw=:(+/*:,s)-sb r=:sb,fb,vb=:sb%fb=:<:{.k s=:sw,fw,vw=:sw%fw=:*/$}."1 y (":r),(":s),:' F =',0.2":vb%vw ) NB. *************** << 5.3 >> *************** decomp2=:3 : 0 V0=:y -M0=.(+/%#),y vc=:|:(|.s=.$y )$(+/%#)|:V0 e=:V0-vc+vr=.s$(+/%#)V0 d=:y ;'=';(s$M0);'+';V0 2 1 5$d,vc;'+';vr;'+';e ) av2=:3 : 0 s=:y -(+/%#),y sc=:+/*:,(|.k=:$y )$(+/%#)|:s sr=:+/*:,k$(+/%#)s ve=:(se=:(+/*:,s)-sc+sr)%fe=:*/<:k r=:":sc,fc,vc,(vc=:sc%fc=:<:{.k)%ve s=:":sr,fr,vr,(vr=:sr%fr=:<:{:k)%ve r,s,:":se,fe,ve ) NB. *************** << 5.5 >> *************** ava0=:3 : 0 V0=:(+/*:X0-M0=:(+/%#)X0)%N0=:$X0=:,y (4+N0*1+^.(o.2)*V0),V0,M0 ) ava1=:3 : 0 M0=:N0,.((N0=:{:$y )*=i.k=:{.$y ),.1 M0=:((k*N0),(k$N0),0),M0,0,k$1 b=:}:((+/r),(r=:+/"1 y ),0)%.M0 V0=:(+/+/"1*:y -({.+}.)b)%N0=:k*N0 ((N0*1+^.(o.2)*V0)++:>:k),V0,b ) NB. *************** << 5.6 >> *************** ava2=:3 : 0 M0=:(k*N0),(k$N0),((N0=:{:$y )$k=:{.$y ),0,0 M0=:M0,N0,.(N0*=i.k),.((k,>:N0)$1),.0 M0=:M0,(k,.((N0,k)$1),.(k*=i.N0),.0),.1 M0=:(M0,0,k$1),((>:k)$0),N0$1 b=:}:}:((+/r),(+/"1 y ),(r=:+/y ),0,0)%.M0 q=:+/*:,y -({.b)+(}.(>:k){.b)+/(-N0){.b ((t*1+^.(o.2)*V0)++:k+N0),(V0=:q%t=:k*N0),b ) ava=:3 : 0 r=.'MODEL M1 : ',0j2":ava0 y r=. r,: 'MODEL M2 : ',0j2":ava1 y r=. r, 'MODEL M3 : ',0j2":ava1 |: y r, 'MODEL M4 : ' ,0j2":ava2 y ) NB. =============================== NB. Stadt 6 NB. =============================== NB. *************** << 6.3 >> *************** add=:1&,.@(|:@]) regb=:[%.add@] ssr=:4 : ' +/*:x -(add y )+/ .*x regb y ' rega=:4 : '(2*1{k)+(^.(x ssr y )%N0)*N0=:0{k=:$add y ' var=:3 : '(<0 1)|:%.(|:w)+/ . *w=:add y ' regt=:4 : 0 (x regb y )%%:(var y )*(x ssr y )%(0{k)-1{k=:$add y ) reg_all=:4 : 0 q=:+/ *: x - w +/ . * b=: x %. w=: 1 ,.|: y c=:100*1-q%+/*:x -(+/%#)x a=:(N0*^.q%N0=:{.N0k)++:k=:{:N0k=:$w t=:b%%:((<0 1)|:%.(|:w)+/ .*w)*q%N0-k q=:'res. variance :',8.3":q%N0 c=:'co. of det.(%):',8.3":c a=:'value of AIC :',8.3":a bt=:'reg-coeff. and t-values:' q,c,a,bt,10.3":b,:t ) reg0=:4 : 0 q=:+/*:x -y *b=:x %.y a=:2+N0*^.q%N0=:#y (q%N0),a,b,b*%:(N0-1)*(+/*:y )%q ) NB. *************** << 6.4 >> *************** dep=:4 : 0 y +/ .*(>:i.#y )^/i.>:x ) indep=:4 : 0 (2$k){.(k,+:k)$+/(>:i.#y )^/i.<:+:k=:>:x ) pregb=:([dep])%.[indep] preg=:4 : 0 b=:y %.w=:(>:i.N0=:#y )^/i.k=:>:x q=:+/*:y -w+/ .*b c=:100*1-q%+/*:y -(+/%#)y a=:(N0*^.q%N0)++:k c=:'co. of det.(%):',7j2":c a=:'value of AIC :',7j2":a c,a,:'value of MLE :',7j2":b ) NB. *************** << 6.5 >> *************** adep=:[}.]-(+/%#)@] aindep=:4 : '|:(0,<:x )}.((x ),<:#y )$y -(+/%#)y ' aregb=:([ adep ])%.[ aindep ] areg=:4 : 0 Y0=:(k=:x )}.t=:y - M0=:(+/%#) y X0=:|:(0,<:k)}. (k,<:N0=:#t)$t q=:+/ *: Y0 - X0 +/ . * b =: Y0 %. X0 c=:1-q%+/*:Y0-(+/%#)Y0 M0,c,((N0*^.q%N0=:N0-k)++:k),b ) NB. ================================== NB. Stadt 7 NB. ================================== mpbm=:3 : 0 d=:%:(4*b=:*:1{y )+*:(a=:0{y )-c=:2{y e=:-:a+c+(1,_1)*d |:e,V0,:%:1-*:V0=:(1,_1)*%:b%b+*:a-e ) itr=:3 : 0 M0=:M0+/ . *M0=:M0%>./|,M0=:M0+/ . *M0=:>{:y (V0%>./|V0=:(>{.y )+/ . *M0);M0 ) mev=:3 : 0 V0=:V0%%:+/*:V0=:>{.itr^:20(1;y ) (+/(y +/ . *V0)%V0*#V0),V0 ) red=:3 : 'y -({.lV0)**/~}.lV0=:mev y ' M3=:3 3$18 0 9 0 6 _3 9 _3 6 evs=:4 : 0 mev"2(red^:(i.x ))y ) NB. *************** << 7.9 >> *************** standm=:3 : 0 X0=:y -(k=:$y )$(+/%#)y X0%k$%:((<0 1)|:(|:X0)+/ .*X0)%{.k ) corm=:3 : '((|:X0)+/ .*X0)%#X0=:standm y ' NB. *************** << 7.10>> *************** pca=:4 : 0 X0=:y -(k=:$y )$(+/%#)y X0=:X0%k$%:((<0 1)|:(|:X0)+/ .*X0)%{.k ev=:x evs ((|:X0)+/ .*X0)%{.k e=:'e-value & vector :',7.3":ev e,'pc-values :',6j2":X0+/ .*}.|:ev ) NB. ===================================== NB. Stadt 8 NB. ===================================== input=:3 : '(1!:1)1' print=:(1!:2)&2 input_ex=: 4 : 0 inputdata=:input'' (