Simulating draws from a negative binomial I am looking for a way to simulate draws from a negative binomial distribution for a computational experiment on biological sequencing data. I am using a high performance package which only has certain distributions however, and though I know that gamma+poisson draws would give me the required simulation, the package lacks the latter. Here is a list of the distributions I have: [uniform, triangular, beta, exponential, gaussian, lognormal, vonmises, weibull, pareto, gamma]. Is there a simple approximation I can use from any of these functions that would require the least computational complexity (i.e. dont loop over creating many random draws for a single sample).

Why don't you use the inverse CDF method? The CDF of the negative binomial is the regularized incomplete beta function, which is just a ratio of beta functions so it should not be a problem to obtain it with your setup. You can see the detailshere and here. If you want something more fancy tailored specifically to the negative binomial distribution, the standard reference is Devroye's book Non-uniform random variate generation.
