# How to implement random sampling with continuous variables?

How functions like rnorm in R (and similar functions) create a random sample ? If I want to implement one algorithm to simulate this procedure what can I do? When you have the pdf or pmf of a distribution how can you use this to create a random sample with a computer? Is there some book on this topic?Is this a numerical analysis topic? I searched alot but I couldn't find any information about this.

• If you can sample a $U(0,1)$ random variable, apply the inverse CDF of a random variable to get a sample of it. For Gaussians there are other options, see for example this question. – Yuval Filmus Apr 8 at 18:44

One standard approach is to use inverse transform sampling: if $$F$$ is the cdf of the desired random variable and $$U$$ is uniformly distributed, then $$F^{-1}(U)$$ has the desired distribution. There are more sophisticated methods for specific distributions; you can find references and links where you can learn more in the linked Wikipedia article.