# 2004 年 11 月 11 日作成
rep.no<-100000
ell.largest<-rep(0,rep.no)
ell.2nd<-rep(0,rep.no)
ell.3rd<-rep(0,rep.no)
ell.smallest<-rep(0,rep.no)
ell.1d<-ell.1;ell.2d<-ell.2
#ell.1; ell.2
for (i in 1:rep.no){
xw.1<-rnorm(10,0,1)
xw.2<-rnorm(10,0,1)
xw.3<-rnorm(10,0,1)
xw.4<-rnorm(10,0,1)
xw<-matrix(c(xw.1,xw.2,xw.3,xw.4),10,4)
#xw
w<-t(xw)%*%xw
#w
eigen.w<-eigen(w)
#eigen.w
lam<-c(eigen.w$values)
hmat<-matrix(eigen.w$vectors,4,4)
#lam; hmat
#ell.largest[i]<-lam[1]/10; ell.2nd[i]<-lam[2]/10; ell.3rd[i]<-lam[3]/10; ell.sm#allest[i]<-lam[4]/10
ell.largest[i]<-lam[1]/13; ell.2nd[i]<-lam[2]/11; ell.3rd[i]<-lam[3]/9; ell.smallest[i]<-lam[4]/7
#ell.largest[i]<-lam[1]/10; ell.smallest[i]<-lam[4]/10
}
plot(density(ell.largest),xlim=c(0,4),ylim=c(0,3.0),xlab="",ylab="",main="density of eigenvalues of Dey(dim=4,n=10)")
par(new=T)
plot(density(ell.2nd),xlim=c(0,4),,xlab="",ylab="",ylim=c(0,3.0),main="")
par(new=T)
plot(density(ell.3rd),xlim=c(0,4),,xlab="",ylab="",ylim=c(0,3.0),main="")
par(new=T)
plot(density(ell.smallest),xlim=c(0,4),,xlab="",ylab="",ylim=c(0,3.0),main="")
mean(ell.1d);mean(ell.2d)
var(ell.1d); mean(ell.2d)
mean(ell.1);mean(ell.2)
var(ell.1); mean(ell.2)