DATA 604 - D10

set.seed(155)
m <- 10000 
x <- numeric(m) 
k <- 0 
u <- runif(m)
for (i in 2:m) { 
xt <- x[i-1]
y <- rnorm(1) 
num <- dcauchy(y)*dnorm((xt),mean=y)
den <- dcauchy(xt)*dnorm((y),mean=xt)
if (u[i] <= num/den) {
  x[i] <- y}
else {
  x[i] <- xt 
  k <- k+1 }

}

x <- x[1001:length(x)]
metQ <-quantile(x,seq(0,1,.1))
cauchyQ <- qcauchy(seq(0,1,.1))

knitr::kable(cbind(metQ,cauchyQ))