Digression - inverse transformation sampling

We can generate data from the standard normal distribution by

data <- rnorm(10000, mean=0, sd=1)
hist(data, breaks=37)

Inverse transformation sampling is a data generation technique using CDF.

It starts from a randomly sampled number from uniform([0, 1]). And, find it’s inverse image through the CDF. As illustrated below, the inverse image will hand between -2 and 2 with high probability.

u <- runif(10000)
hist(qnorm(u), breaks=37)