Simulating from a gamma distribution with small shape parameter

TL;DR

This paper introduces a new, highly efficient acceptance-rejection algorithm for simulating gamma distributions with small shape parameters, leveraging a limiting distribution to improve performance over existing methods.

Contribution

The paper develops a novel acceptance-rejection algorithm based on a limiting distribution for small shape gamma distributions, enhancing simulation efficiency.

Findings

The new algorithm has higher acceptance rates than existing methods.

The limiting distribution provides valuable insight for constructing efficient samplers.

The proposed method outperforms traditional algorithms in simulation speed.

Abstract

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.