Simulating from a gamma distribution with small shape parameter

Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we 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. Comparisons based on acceptance rates show that the proposed procedure is more efficient than existing acceptance–rejection methods.