library(copula) d<-2 family="clayton" n<-2000 param<-4 c.cop<-archmCopula(family=family,param=param,dim=d) set.seed(3) dendat<-rcopula(c.cop, n) df<-4 dendat<-qt(dendat, df=df) mpoint<-matrix(0,1,d) for (i in 1:d) mpoint[1,i]<-mean(dendat[,i]) rad<-2 dendat2<-matrix(0,n,d) found<-0 for (i in 1:n){ point<-dendat[i,] distan<-sqrt(sum((point-mpoint)^2)) if (distan>rad){ found<-found+1 dendat2[found,]<-point } } dendat2<-dendat2[1:found,] rad<-6.5 dendat3<-matrix(0,n,d) found<-0 for (i in 1:n){ point<-dendat[i,] distan<-sqrt(sum((point-mpoint)^2)) if (distan>rad){ found<-found+1 dendat3[found,]<-point } } dendat3<-dendat3[1:found,] # frame 1 ru<-11 rl<--7 plot(dendat,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") # frame 2 plot(dendat2,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") # frame 3 plot(dendat3,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2")
library(copula) d<-2 family="clayton" n<-2000 param<-4 c.cop<-archmCopula(family=family,param=param,dim=d) set.seed(3) dendat<-rcopula(c.cop, n) df<-4 dendat<-qt(dendat, df=df) rho<-1.1 tt<-leafsfirst(dendat=dendat,rho=rho) paletti<-c("red","blue","green", "orange","navy","darkgreen", "orchid","aquamarine","turquoise", "pink","violet","magenta","chocolate","cyan", colors()[50:657],colors()[50:657]) # frame 1 ru<-11 rl<--7 ts<-tree.segme(tt,paletti=paletti) plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") text(-4.8,-6,labels="T1",cex=1.5) text(-0.3,9,labels="T2",cex=1.5) text(10,3,labels="T3",cex=1.5) # frame 2 plottree(tt,modelabel=TRUE,colo=TRUE,paletti=paletti,#col=col,linecol=col, ptext=0.6,symbo="T",cex=1.5, xmarginright=0.05,xmarginleft=0.05)
d<-2 n<-11 dendat<-matrix(0,n,d) dendat[1,]<-c(0,0) # upper tail dendat[2,]<-c(0,1) dendat[3,]<-c(0,2) dendat[4,]<-c(0,3) # left ear dendat[5,]<-c(-1,3.6) # right ear dendat[6,]<-c(1,4) # lower tail dendat[7,]<-c(-0.1,-1.2) dendat[8,]<-c(-0.1,-2) dendat[9,]<-c(-0.1,-2.8) # nose dendat[10,]<-c(0.8,0) dendat[11,]<-c(2,0) refe<-c(0,0) rho2<-0.75 tt2<-leafsfirst(dendat=dendat,rho=rho2,refe=refe) tt.illu<-tt2 paletti<-c("red","blue","green", "orange","navy","darkgreen", "orchid","aquamarine","turquoise", "pink","violet","magenta","chocolate","cyan") col<-colobary(tt2$parent,paletti) epsi<-0.0000001 ota1<-c(2,3,4,5,6,7,8,9,11) ota2<-c(5,6) # frame 1 plot(dendat[tt2$infopoint,],col=col,xlab="coordinate 1",ylab="coordinate 2", pch=19,cex=2) #,xlim=c(-3,3),ylim=c(-3,3)) for (i in 1:n){ z<-dendat[i,] ala<-z[1]-rho2+epsi yla<-z[1]+rho2-epsi curve(sqrt(rho2^2-(x-z[1])^2)+z[2],add=TRUE,xlim=c(ala,yla)) curve(-sqrt(rho2^2-(x-z[1])^2)+z[2],add=TRUE,xlim=c(ala,yla)) } # frame 2 plot(dendat[tt2$infopoint,],col=col,xlab="coordinate 1",ylab="coordinate 2", pch=19,cex=2) #,xlim=c(-3,3),ylim=c(-3,3)) for (i in ota1){ z<-dendat[i,] ala<-z[1]-rho2+epsi yla<-z[1]+rho2-epsi curve(sqrt(rho2^2-(x-z[1])^2)+z[2],add=TRUE,xlim=c(ala,yla)) curve(-sqrt(rho2^2-(x-z[1])^2)+z[2],add=TRUE,xlim=c(ala,yla)) } # frame 3 plot(dendat[tt2$infopoint,],col=col,xlab="coordinate 1",ylab="coordinate 2", pch=19,cex=2) #,xlim=c(-3,3),ylim=c(-3,3)) for (i in ota2){ z<-dendat[i,] ala<-z[1]-rho2+epsi yla<-z[1]+rho2-epsi curve(sqrt(rho2^2-(x-z[1])^2)+z[2],add=TRUE,xlim=c(ala,yla)) curve(-sqrt(rho2^2-(x-z[1])^2)+z[2],add=TRUE,xlim=c(ala,yla)) } # frame 4 plottree(tt2,col=col,ptext=0.2,pch=19,linecol=col, xmarginleft=0.1,xmarginright=0.1,symbo="T", cex=1.5,nodemag=1.5,linemag=2)
library(copula) d<-2 family="clayton" n<-2000 param<-4 c.cop<-archmCopula(family=family,param=param,dim=d) set.seed(3) dendat<-rcopula(c.cop, n) df<-4 dendat<-qt(dendat, df=df) rho<-1.1 tt<-leafsfirst(dendat=dendat,rho=rho) # frame 1 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.6) # frame 2 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.6)
d<-2 n<-11 dendat<-matrix(0,n,d) dendat[1,]<-c(0,0) # upper tail dendat[2,]<-c(0,1) dendat[3,]<-c(0,2) dendat[4,]<-c(0,3) # left ear dendat[5,]<-c(-1,3.6) # right ear dendat[6,]<-c(1,4) # lower tail dendat[7,]<-c(-0.1,-1.2) dendat[8,]<-c(-0.1,-2) dendat[9,]<-c(-0.1,-2.8) # nose dendat[10,]<-c(0.8,0) dendat[11,]<-c(2,0) refe<-c(0,0) rho2<-0.75 tt2<-leafsfirst(dendat=dendat,rho=rho2,refe=refe) # frame 1 plotbary(tt2,coordi=1,ptext=0.2,symbo="T") # frame 2 plotbary(tt2,coordi=2,ptext=0.2,symbo="T")
sympoli<-seq(20,25,1) # ball slices dendat.slice<-matrix(0,1000,2) culot<-matrix(0,1000,1) sympot<-matrix(0,1000,1) level<-matrix(0,1000,1) step<-0.1 yyt<-c(-0.9,-0.5,0,0.4,0.8) cur<-0 for (i in 1:length(yyt)){ y<-yyt[i] xbeg<--sqrt(1-y^2) xend<-sqrt(1-y^2) x<-seq(xbeg,xend,step) dendat.slice[(cur+1):(cur+length(x)),1]<-x dendat.slice[(cur+1):(cur+length(x)),2]<-y culot[(cur+1):(cur+length(x))]<-i sympot[(cur+1):(cur+length(x))]<-sympoli[i] level[(cur+1):(cur+length(x))]<-sqrt(x^2+y^2) cur<-cur+length(x) } dendat.slice<-dendat.slice[1:cur,] culot<-culot[1:cur] sympot<-sympot[1:cur] level<-level[1:cur] # frame 1 plot(dendat.slice,xlim=c(-1,1),ylim=c(-1,1),col=culot,pch=sympot, xlab="coordinate 1",ylab="coordinate 2",cex=1.5) curve(sqrt(1^2-x^2),add=TRUE,xlim=c(-1,1)) curve(-sqrt(1^2-x^2),add=TRUE,xlim=c(-1,1)) # frame 2 plot(dendat.slice[,1],level,col=culot,pch=sympot,xlab="coordinate 1",cex=1.5) # frame 3 plot(dendat.slice[,2],level,col=culot,pch=sympot,xlab="coordinate 2",cex=1.5)
sympoli<-seq(20,25,1) # ball spheres r<-c(0.2,0.4,0.6,0.8,1) theta<-seq(0.1,2*pi,0.2) n<-length(r)*length(theta) dendat.spheres<-matrix(0,n,2) lavel<-matrix(0,n,1) calot<-matrix(0,n,1) sympot<-matrix(0,n,1) ind<-0 for (i in 1:length(r)){ for (j in 1:length(theta)){ x<-r[i]*cos(theta[j]) y<-r[i]*sin(theta[j]) ind<-ind+1 dendat.spheres[ind,1]<-x dendat.spheres[ind,2]<-y lavel[ind]<-r[i] calot[ind]<-i sympot[ind]<-sympoli[i] } } # frame 1 plot(dendat.spheres,col=calot,pch=sympot,cex=1.5, xlab="coordinate 1",ylab="coordinate 2") # frame 2 plot(dendat.spheres[,1],lavel,ylim=c(0,1),col=calot,pch=sympot,cex=1.5, xlab="coordinate 1",ylab="level") # frame 3 plot(dendat.spheres[,2],lavel,ylim=c(0,1),col=calot,pch=sympot,cex=1.5, xlab="coordinate 2",ylab="level")
library(copula) g<-5 seed<-5 n<-2000 family="frank" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1.1 tt<-leafsfirst(dendat=dendat,rho=rho) # frame 1 plotbary(tt,coordi=1) # frame 2 plotbary(tt,coordi=1,lines=FALSE)
seed<-1 type<-"cross" n<-1000 d<-2 dendat<-sim.data(n=n,type=type,seed=seed) cente<-c(mean(dendat[,1]),mean(dendat[,2])) level2<-sqrt(pituus(dendat-cente)) rho<-0.65 tt<-leafsfirst(dendat=dendat,rho=rho) # frame 1 i<-1 plot(dendat[,i],level2,ylab="level",xlab="") title(sub=paste("coordinate",as.character(i))) # frame 2 i<-2 plot(dendat[,i],level2,ylab="level",xlab="") title(sub=paste("coordinate",as.character(i))) # frame 3 plotbary(tt,modelabel=FALSE,paletti=seq(1:2000)) # frame 4 plotbary(tt,coordi=2,modelabel=FALSE,paletti=seq(1:2000))
# Ball seed<-1 n<-1000 d<-2 dendat.ball<-matrix(0,n,d) set.seed(seed) nolla<-rep(0,d) saatu<-0 while (saatuFigure 11
d<-2 mixnum<-1 M<-matrix(0,mixnum,d) sig<-matrix(1,mixnum,d) p<-matrix(1,mixnum,1) p<-p/sum(p) n<-2000 sig[1,1]<-2 dendat<-sim.data(n,M=M,sig=sig,p=p,seed=1,type="mixt") rot45<-matrix(0,d,d) basis1<-c(1,1) basis2<-c(-1,1) basis1<-basis1/sqrt(sum(basis1^2)) basis2<-basis2/sqrt(sum(basis2^2)) rot45[,1]<-basis1 rot45[,2]<-basis2 rho<-1.4 paletti<-c("red","blue","green", "orange","navy","darkgreen", "orchid","aquamarine","turquoise", "pink","violet","magenta","chocolate","cyan", colors()[50:657],colors()[50:657]) # frame 1 dendat.rot<-dendat%*%rot45 dendat<-dendat.rot tt<-leafsfirst(dendat=dendat,rho=rho) r<-7 ts<-tree.segme(tt,paletti=paletti) plot(dendat,col=ts,xlim=c(-r,r),ylim=c(-r,r), xlab="coordinate 1",ylab="coordinate 2") text(5,-5,"T2");text(-5,5,"T1") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3) # frame 4 dendat.rot<-dendat%*%rot45 dendat<-dendat.rot tt<-leafsfirst(dendat=dendat,rho=rho) r<-7 ts<-tree.segme(tt,paletti=paletti) plot(dendat,col=ts,xlim=c(-r,r),ylim=c(-r,r), xlab="coordinate 1",ylab="coordinate 2") text(0,-6.8,"T2");text(-0.1,6.8,"T1") # frame 5 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 6 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3) # frame 7 dendat.rot<-dendat%*%rot45 dendat<-dendat.rot tt<-leafsfirst(dendat=dendat,rho=rho) r<-7 ts<-tree.segme(tt,paletti=paletti) plot(dendat,col=ts,xlim=c(-r,r),ylim=c(-r,r), xlab="coordinate 1",ylab="coordinate 2") text(-5,-5,"21");text(5,5,"T1") # frame 8 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 9 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 12
r<-0 cova<-matrix(1,2,2) cova[1,2]<-r cova[2,1]<-r t<-4 seed<-3 n<-1000 dendat<-sim.data(n=n,cova=cova,type="gauss",marginal="student",t=t,seed=seed) rl<-min(dendat) ru<-max(dendat) rho<-1.5 tt<-leafsfirst(dendat=dendat,rho=rho) ts<-tree.segme(tt) # frame 1 plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") #for (i in 1:dim(mc)[1]) text(mc[i,1],mc[i,2],"T1") text(1,-6,"T4") text(8,-0,"T2") text(0,9,"T1") text(-6,0,"T3") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 13
r<-0.5 cova<-matrix(1,2,2) cova[1,2]<-r cova[2,1]<-r t<-3 seed<-4 n<-1000 dendat<-sim.data(n=n,cova=cova,type="gauss",marginal="student",t=t,seed=seed) rl<-min(dendat) ru<-max(dendat) rho<-1.6 tt<-leafsfirst(dendat=dendat,rho=rho) ts<-tree.segme(tt) # frame 1 plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") text(1,-9,"T3") text(9,-0,"T1") text(0,9,"T2") text(-9,0,"T4") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 14
r<-0.6 cova<-matrix(1,2,2) cova[1,2]<-r cova[2,1]<-r n<-1000 seed<-2 t<-2 dendat<-sim.data(n=n,cova=cova,type="student",marginal="gauss",df=t,seed=seed) rl<-min(dendat) ru<-max(dendat) rho<-1 tt<-leafsfirst(dendat=dendat,rho=rho) ts<-tree.segme(tt) # frame 1 plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") text(-3,-3,"T4") text(3,-3,"T3") text(3.3,3.3,"T1") text(-3,3,"T2") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 15
library(copula) g<-4 seed<-2 n<-1000 family="clayton" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1 tt<-leafsfirst(dendat=dendat,rho=rho) ts<-tree.segme(tt) # frame 1 plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") text(-3,-3.2,"T1") text(3,3,"T2") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 16
library(copula) g<-3 seed<-2 n<-1000 family="gumbel" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) mean(dendat[,1]) mean(dendat[,2]) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1 tt<-leafsfirst(dendat=dendat,rho=rho) ts<-tree.segme(tt) # frame 1 plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") text(-3,-3.2,"T2") text(2.8,3.2,"T1") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 17
library(copula) g<-5 seed<-5 n<-2000 family="frank" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) mean(dendat[,1]) mean(dendat[,2]) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1.1 tt<-leafsfirst(dendat=dendat,rho=rho) ts<-tree.segme(tt) # frame 1 plot(dendat,col=ts,xlim=c(rl,ru),ylim=c(rl,ru), xlab="coordinate 1",ylab="coordinate 2") text(-3,-3.2,"T2") text(2.8,3.2,"T1") # frame 2 plotbary(tt,coordi=1,modelabel=TRUE,symbo="T",ptext=0.3) # frame 3 plotbary(tt,coordi=2,modelabel=TRUE,symbo="T",ptext=0.3)Figure 18
library(copula) d<-2 family="clayton" n<-2000 param<-4 c.cop<-archmCopula(family=family,param=param,dim=d) set.seed(3) dendat<-rcopula(c.cop, n) df<-4 dendat<-qt(dendat, df=df) rho<-1.1 tt<-leafsfirst(dendat=dendat,rho=rho) # frame 1 plotvolu(tt,colo=TRUE,modelabel=TRUE,symbo="T",ptext=0.5,cex=1.5) # frame 2 plotvolu(tt,colo=TRUE,modelabel=TRUE,xlim=c(1130,1170), symbo="T",ptext=0.5,cex=1.5)Figure 19
d<-2 n<-11 dendat<-matrix(0,n,d) dendat[1,]<-c(0,0) # upper tail dendat[2,]<-c(0,1) dendat[3,]<-c(0,2) dendat[4,]<-c(0,3) # left ear dendat[5,]<-c(-1,3.6) # right ear dendat[6,]<-c(1,4) # lower tail dendat[7,]<-c(-0.1,-1.2) dendat[8,]<-c(-0.1,-2) dendat[9,]<-c(-0.1,-2.8) # nose dendat[10,]<-c(0.8,0) dendat[11,]<-c(2,0) refe<-c(0,0) rho2<-0.75 tt2<-leafsfirst(dendat=dendat,rho=rho2,refe=refe) # frame plotvolu(tt2,ptext=0.2,symbo="T",colo=TRUE,modelabel=TRUE,cex=1.5)Figure 20
# Ball seed<-1 n<-1000 d<-2 dendat.ball<-matrix(0,n,d) set.seed(seed) nolla<-rep(0,d) saatu<-0 while (saatuFigure 21
r<-0 cova<-matrix(1,2,2) cova[1,2]<-r cova[2,1]<-r t<-4 seed<-3 n<-1000 dendat<-sim.data(n=n,cova=cova,type="gauss",marginal="student",t=t,seed=seed) rl<-min(dendat) ru<-max(dendat) rho<-1.5 tt.gaussr0<-leafsfirst(dendat=dendat,rho=rho) r<-0.5 cova<-matrix(1,2,2) cova[1,2]<-r cova[2,1]<-r t<-3 seed<-4 n<-1000 dendat<-sim.data(n=n,cova=cova,type="gauss",marginal="student",t=t,seed=seed) rl<-min(dendat) ru<-max(dendat) rho<-1.6 tt.gaussr5<-leafsfirst(dendat=dendat,rho=rho) r<-0.6 cova<-matrix(1,2,2) cova[1,2]<-r cova[2,1]<-r n<-1000 seed<-2 t<-2 dendat<-sim.data(n=n,cova=cova,type="student",marginal="gauss",df=t,seed=seed) rl<-min(dendat) ru<-max(dendat) rho<-1 tt.student<-leafsfirst(dendat=dendat,rho=rho) # frame 1 plotvolu(tt.gaussr0,modelabel=FALSE,colo=TRUE) # frame 2 plotvolu(tt.gaussr5,modelabel=FALSE,colo=TRUE) # frame 3 plotvolu(tt.student,modelabel=FALSE,colo=TRUE) # frame 4 plotvolu(tt.gaussr0,modelabel=FALSE,colo=TRUE,xlim=c(450,550)) # frame 5 plotvolu(tt.gaussr5,modelabel=FALSE,colo=TRUE,xlim=c(440,560)) # frame 6 plotvolu(tt.student,modelabel=FALSE,colo=TRUE,xlim=c(440,560))Figure 22
library(copula) g<-4 seed<-2 n<-1000 family="clayton" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1 tt<-leafsfirst(dendat=dendat,rho=rho) tt.clayton<-tt g<-3 seed<-2 n<-1000 family="gumbel" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1 tt.gumbel<-leafsfirst(dendat=dendat,rho=rho) g<-5 seed<-5 n<-2000 family="frank" c.cop<-archmCopula(family, param=g, dim=2) set.seed(seed) dendat<-rcopula(c.cop, n=n) dendat<-qnorm(dendat) rl<-min(dendat) ru<-max(dendat) rho<-1.1 tt.frank<-leafsfirst(dendat=dendat,rho=rho) # frame 1 plotvolu(tt.clayton,modelabel=FALSE,colo=TRUE) # frame 2 plotvolu(tt.gumbel,modelabel=FALSE,colo=TRUE) # frame 3 plotvolu(tt.frank,modelabel=FALSE,colo=TRUE)