##### R-code for making Figure 6.2

set.seed(1000)

T1jn = rep(0,100)  ### This is |T_jn| used in (6.20) 
                   ### when the process is IC
T2jn = rep(0,100)  ### This is |T_jn| used in (6.20)
                   ### when the process is OC

x = rnorm(100,0,1)
n=length(x)

### Compute the sequence of {|T1_jn|, 1 <= j <= n-1} to
### show that it has a U-shape when the process is IC

for(j in 1:(n-1)){

    T1jn[j] = sqrt(j*(n-j)/n)*abs(mean(x[1:j])-mean(x[(j+1):n]))/
              sqrt(var(x[1:j])*(j-1)+var(x[(j+1):n])*(n-j-1))

}

### Compute the sequence of {|T2_jn|, 1 <= j <= n-1} to
### show that it has a power to detect a shift when the 
### process is OC

y=x+c(rep(0,50),rep(1,50))

for(j in 1:(n-1)){

    T2jn[j] = sqrt(j*(n-j)/n)*abs(mean(y[1:j])-mean(y[(j+1):n]))/
              sqrt(var(y[1:j])*(j-1)+var(y[(j+1):n])*(n-j-1))

}


### Make a figure

postscript("fig62.ps",width=6.5,height=6.5,horizontal=F)

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

i=seq(1,n)

plot(i,x,type="o",lty=1,pch=16,xlab="n",
     ylab=expression(X[n]),mgp=c(2,1,0),xlim=c(0,n), 
     ylim=c(-2.6,2.6), cex=0.8)
title(xlab="(a)",cex=0.9)

plot(i[2:(n-1)],T1jn[2:(n-1)],type="o",lty=1,pch=16,xlab="n",
     ylab=expression(group("|",T[jn],"|")),mgp=c(2,1,0),xlim=c(1,n), 
     ylim=c(0,0.4), cex=0.8)
title(xlab="(b)",cex=0.9)

plot(i,y,type="o",lty=1,pch=16,xlab="n",
     ylab=expression(X[n]),mgp=c(2,1,0),xlim=c(0,n), 
     ylim=c(-2.6,3.6), cex=0.8)
title(xlab="(c)",cex=0.9)

plot(i[2:(n-1)],T2jn[2:(n-1)],type="o",lty=1,pch=16,xlab="n",
     ylab=expression(group("|",T[jn],"|")),mgp=c(2,1,0),xlim=c(1,n), 
     ylim=c(0,0.8), cex=0.8)
title(xlab="(d)",cex=0.9)

graphics.off()