Inverse transform sampling (also known as inversion sampling, the inverse probability integral
transform, the inverse transformation method, Smirnov transform, golden rule, etc.)
is a basic method for pseudo-random number sampling,
i.e. for generating sample numbers at random from any probability distribution given its
cumulative distribution function.
This basic idea is this:
to generate a random variable X with a cumulative distribution function F(x) for
we first sample u from the uniform distribution.
Then, x = F-1(u) = Q(u).
This method requires that F(x) has a continuous density function,
hence, strictly increasing and its inverse well defined.
"Paul Glasserman. "p. 44," Monte Carlo Methods in Financial Engineering, 2004."