On the gamma distribution with small shape parameter
The gamma distribution with small shape parameter is difficult to characterize. In particular, standard algorithms for sampling from such a distribution often fail, so something special is needed. In this paper, we first obtain a limiting distribution for a suitably normalized gamma distribution when the shape parameter tends to zero. Then this limiting distribution provides insight to the construction of a new, simple, and highly efficient acceptance--rejection algorithm. Pseudo-code, and an R implementation, for this new sampling algorithm are provided.