As I mentioned in a recent post, I’ve just received a copy of Advanced Markov Chain Monte Carlo Methods. Chapter 1.4 in the book (very quickly) covers random variable generation. Inverse CDF Method A standard algorithm for generating random numbers is the inverse cdf method. The continuous version of the algorithm is as follows: 1. 
Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).
