Inverse transform sampling

[timueh]

It would be helpful to transpile the inverse transform sampling method from here to our package. Yes, I am aware that there is a working implementation withing ApproxFun.jl, but we would like to avoid having to add this heavy dependency (load up time increases drastically.).

p.s.: the implementation withing ApproxFun.jl can be found here.

[timueh]

This is the paper the algorithm is based on. At the beginning of Section 2 the authors say

Let $f(x)$ be a prescribed non-negative function supported on the interval $[a, b]$. Otherwise, if the support of $f$ is the whole real line and $f$ is rapidly decaying, an interval $[a, b]$ can be selected outside of which $f$ is negligible.

just something to bear in mind.

[adriangrupp]

Since this issue is already two years old, one should first verify, if the load up time improved.
If not, check if we can just use ApproxFunBase.jl instead. However,
the stand-alone usage is not documented yet.