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Efficient simulation from a gamma distribution with small shape parameter

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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. The proposed method is fast and comparisons based on acceptance rates show that it is more efficient than existing acceptance–rejection methods.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Statistics, Purdue University, West Lafayette, IN, USA

    Chuanhai Liu

  2. Department of Statistics, North Carolina State University, Raleigh, NC, USA

    Ryan Martin & Nick Syring

Authors
  1. Chuanhai Liu
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  2. Ryan Martin
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  3. Nick Syring
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Correspondence to Ryan Martin.

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Liu, C., Martin, R. & Syring, N. Efficient simulation from a gamma distribution with small shape parameter. Comput Stat 32, 1767–1775 (2017). https://doi.org/10.1007/s00180-016-0692-0

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  • DOI: https://doi.org/10.1007/s00180-016-0692-0

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