ImpSamp=function(n,nu){
# The normal simulation has not been converging when the variance is nu/(nu-2).
# A variance of nu/2 is used here, but still performs poorly and the normal
# simulation should probably be removed from the simulation
s1=rnorm(n,0,sqrt(nu/(nu-2.0)))
s2=rcauchy(n)
s3=rt(n,nu)
h1=sqrt(abs(s1/(1.0-s1)))
h2=sqrt(abs(s2/(1.0-s2)))
h3=sqrt(abs(s3/(1.0-s3)))
# Form the integrands
i1=h1*dt(s1,nu)/dnorm(s1,0,sqrt(nu/(nu-2.0)))
i2=h2*dt(s2,nu)/dcauchy(s2)
i3=h3
# Form the accumulated integrals
t1= cumsum(i1)/seq(1,n)
t2=cumsum(i2)/seq(1,n)
t3=cumsum(i3)/seq(1,n)
win.graph()
ts.plot(as.ts(t1),as.ts(t2),as.ts(t3),xlab="Simulations",ylab="MC Estimate",ylim=c(0,2),lty=c(1,2,3),
 col=c("black","blue","green"))
legend(.7*n,2,c("Normal","Cauchy","t"),col=c("black","blue","green"),lty=c(1,2,3))
abline(h=1.13,col="red")
out=list(t1[n],t2[n],t3[n])
names(out)=c("Normal Estimate","Cauchy Estimate","t Estimate")
out
}