63
> n:=20: muX:=10: sigmaX:=2: muV:=0: sigmaV:=2:
> x:=[random[normald[muX,sigmaX]](n)]:
> v:=[random[normald[muV,sigmaV]](n)]:
> y:=x+v:
> pxy:=[[x[i],y[i]] $i=1..n]:
> plot(pxy,style=point,symbol=circle);
> Mx:=1/n*sum(x[i],i=1..n);
> Dx:=1/n*sum((x[i]-Mx)^2,i=1..n); Sx:=sqrt(Dx);
> My:=1/n*sum(y[i],i=1..n);
> Dy:=1/n*sum((y[i]-My)^2,i=1..n); Sy:=sqrt(Dy);
> Kxy:=1/n*sum(x[i]*y[i]-Mx*My,i=1..n);
> r:=Kxy/Sx/Sy; b1:=r*Sy/Sx; b2:=r*Sx/Sy;
> Y:=evalm(My+b1*(x-Mx)): X:=evalm(Mx+b2*(y-My)):
> pxY:=[[x[i],Y[i]] $i=1..n]:
> pXy:=[[X[i],y[i]] $i=1..n]:
> plot([pxy,pxY,pXy,[[Mx,My]]],style=[point,line,
line,point],symbol=circle,color=[red,green,blue,
black],symbolsize=[10,10,10,20]);
> beta:=0.95: S:=evalf((1-r^2)/sqrt(n)):
> fn:=(x,mu,sigma)->
> exp(-(x-mu)^2/2/sigma^2)/sqrt(2*Pi*sigma^2):
> CInt:=proc(mu,sigma)
> local z,dz,x,y;
> z:=solve(2*int(fn(x,mu,sigma),x=0..y)-beta,y);
> dz:=z*sqrt(sigma/n);
> RETURN([mu-dz,mu+dz]);
> end:
> 'r'=r, CInt(r,S);
> 'b1'=b1, CInt(b1,S*Sy/Sx);
> 'b2'=b2, CInt(b2,S*Sx/Sy);
Пример 6.3 (Mathematica)
<<Graphics`Colors`
<<Statistics`ContinuousDistributions`
n=20; muX=10; sigmaX=2; muV=0; sigmaV=2;
x=RandomArray[NormalDistribution[muX,sigmaX],n];
v=RandomArray[NormalDistribution[muV,sigmaV],n];
y=x+v;
pxy=Transpose[{x,y}];
p1=ListPlot[pxy,PlotStyle->{Red,PointSize[.03]}];
Mx=1/n*Apply[Plus,x]
Dx=1/n*Apply[Plus,(x-Mx)^2]
Sx=Sqrt[Dx]
64
My=1/n*Apply[Plus,y]
Dy=1/n*Apply[Plus,(y-My)^2]
Sy=Sqrt[Dy]
Kxy=1/n*Apply[Plus,x*y-Mx*My]
r=Kxy/Sx/Sy
b1=r*Sy/Sx
b2=r*Sx/Sy
Y=My+b1*(x-Mx); X=Mx+b2*(y-My);
pxY=Transpose[{x,Y}]; pXy=Transpose[{X,y}];
p2=ListPlot[pxY,PlotStyle->{Blue},
PlotJoined->True];
p3=ListPlot[pXy,PlotStyle->{Green},
PlotJoined->True];
p4=ListPlot[{{Mx,My}},
PlotStyle->{Black,PointSize[.05]}];
Show[{p1,p2,p3,p4}];
beta=0.95; S=(1-r^2)/Sqrt[n];
CInt[mu_,sigma_]:=Module[{z,dz},z=y1/.FindRoot[
2*CDF[NormalDistribution[mu,sigma],y1]-beta==0,
{y1,mu}][[1]];dz=z*Sqrt[sigma/n];
{mu-dz,mu+dz}];
Print["r=",r," ",CInt[r,S]]
Print["b1=",b1," ",CInt[b1,S*Sy/Sx]]
Print["b2=",b2," ",CInt[b2,S*Sx/Sy]]
Пример 6.4 (Matlab)
function lab6
n=20; muX=10; sigmaX=2; muV=0; sigmaV=2;
x=normrnd(muX,sigmaX,1,n);
v=normrnd(muV,sigmaV,1,n);
y=x+v;
plot(x,y,'ro'), pause
Mx=1/n*sum(x), Dx=1/n*sum((x-Mx).^2), Sx=sqrt(Dx)
My=1/n*sum(y), Dy=1/n*sum((y-My).^2), Sy=sqrt(Dy)
Kxy=1/n*sum(x.*y-Mx*My)
r=Kxy/Sx/Sy, b1=r*Sy/Sx, b2=r*Sx/Sy
x1=min(x):0.1:max(x); y1=min(y):0.1:max(y);
Y=My+b1*(x1-Mx); X=Mx+b2*(y1-My);
plot(x,y,'ro',x1,Y,'b',X,y1,'g',Mx,My,'kd'), pause
beta=0.95; S=(1-r^2)/sqrt(n);
rCI=CInt(r,S,beta,n); r, rCI
b1CI=CInt(b1,S*Sy/Sx,beta,n); b1, b1CI
b2CI=CInt(b2,S*Sx/Sy,beta,n); b2, b2CI