#####   R-code for making Figure 5.6. It also generates
#####   the data file "example54.dat" used in Example 5.4

set.seed(100)

x = c(rnorm(50,0,1),rnorm(50,0.5,1))

xbar = rep(0,20)
for(i in 1:20){
   xbar[i] = mean(x[((i-1)*5+1):(i*5)])
}

write.table(list(x,xbar),"example54.dat",row.names=F,col.names=F)

postscript("fig56.ps",width=6.5,height=6.5,horizontal=F)

par(mfrow=c(2,2), mar=c(4,4,2,2))

k=0.25
h=5.597

cn1 = rep(0,100)
cn1[1] = max(0,x[1]-k)

for(i in 2:100){
   cn1[i] <- max(0,cn1[i-1]+x[i]-k)
}

ii=seq(1,100)

plot(ii,cn1,type="o",lty=1,pch=16,xlab="n",
     ylab=expression(C[n]^{"+"}),mgp=c(2,1,0),xlim=c(0,100), 
     ylim=c(0,12), cex=0.8)
lines(ii,rep(h,100),lty=2,cex=0.8)
title(xlab="(a)",cex=0.9)

cn2 = rep(0,20)
cn2[1] = max(0,xbar[1]*sqrt(5)-k)

for(i in 2:20){
   cn2[i] <- max(0,cn2[i-1]+xbar[i]*sqrt(5)-k)
}

ii = seq(1,20)

plot(ii,cn2,type="o",lty=1,pch=16,xlab="n",
     ylab=expression(C[n]^{"+"}),mgp=c(2,1,0),xlim=c(0,20), 
     ylim=c(0,12),cex=0.8)
lines(ii,rep(h,20),lty=2,cex=0.8)
title(xlab="(b)",cex=0.9)

la=0.1
rho=2.454

En1=rep(0,100)

En1[1] = la*x[1]+(1-la)*0
for(i in 2:100){
   En1[i] <- la*x[i]+(1-la)*En1[i-1]
}

ii=seq(1,100)
U=rho*sqrt(la/(2-la))
L=-rho*sqrt(la/(2-la))

plot(ii,En1,type="o",lty=1,pch=16,xlab="n",
     ylab=expression(E[n]),mgp=c(2,1,0),xlim=c(0,100), 
     ylim=c(-1,1), cex=0.8)
lines(ii,rep(U,100),lty=2,cex=0.8)
lines(ii,rep(L,100),lty=2,cex=0.8)
title(xlab="(c)",cex=0.9)

En2=rep(0,20)

En2[1] = la*xbar[1]*sqrt(5)+(1-la)*0
for(i in 2:20){
   En2[i] <- la*xbar[i]*sqrt(5)+(1-la)*En2[i-1]
}

ii=seq(1,20)
U=rho*sqrt(la/(2-la))
L=-rho*sqrt(la/(2-la))

plot(ii,En2,type="o",lty=1,pch=16,xlab="n",
     ylab=expression(E[n]),mgp=c(2,1,0),xlim=c(0,20), 
     ylim=c(-1,1),cex=0.8)
lines(ii,rep(U,20),lty=2,cex=0.8)
lines(ii,rep(L,20),lty=2,cex=0.8)
title(xlab="(d)",cex=0.9)

graphics.off()