This function demonstrates the advantage of ratio estimation when further information (ratio) about x and y is available.
From this demonstration we can clearly see that the ratio estimation is generally better than the simple sample average when the ratio R really exists, otherwise ratio estimation may not help.
library(animation)
ani.options(interval = 1, nmax = 50)
## observe the location of the red line (closer to the population mean)
res = sample.ratio()
## absolute difference with the true mean
matplot(abs(cbind(res$ybar.ratio, res$ybar.simple) - res$Ybar), type = "l")
legend("topleft", c("Ratio Estimation", "Sample Average"), lty = 1:2, col = 1:2)
## if the ratio does not actually exist:
sample.ratio(X = rnorm(50), Y = rnorm(50))
## ratio estimation may not be better than the simple average
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