Efficient simulation from a gamma distribution with small shape parameter
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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. The proposed method is fast and comparisons based on acceptance rates show that it is more efficient than existing acceptance–rejection methods.
KeywordsAcceptance rate Acceptance–rejection method Asymptotic distribution Exponential distribution R software
The authors thank the anonymous reviewers for their helpful comments on a previous version of this manuscript. This work was partially supported by the U.S. National Science Foundation, Grants DMS–1208833 and DMS–1208841.
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