Scalable random number generation for truncated log-concave distributions

Inverse transform sampling is an exceptionally general method to generate non-uniform-distributed random numbers, but can be rather unstable when simulating extremely truncated distributions. Many famous probability models share a property called log-concavity, which is not affected by truncation, so they can all be simulated via rejection sampling using Devroye's approach. This sampler is based on rejection and thus more stable than inverse transform, and uses a very simple envelope whose acceptance rate is guaranteed to be at least 20\%. The aim of this paper is threefold: firstly, to warn against the risk of wrongly simulating from truncated distributions; secondly, to motivate a more extensive use of rejection sampling to mitigate the issues; lastly, to motivate Devroye's automatic method as a practical standard in the case of log-concave distributions. We illustrate the proposal by means of simulations based on some Tweedie distributions, for their relevance in regression analysis.