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).

Here is a screenshot of a reference by NL Johnson et al. (2005) summarising the possible approaches based on a Geometric sampling:

Devroye (1985) indeed does not cover any other algorithm than the Gamma-Poisson version. Note that generating a Poisson variate is feasible from the Exponential generator, due to the connection between the Poisson process and the Exponential distribution. It is however not the recommended algorithm.
