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Efficient simulation from a gamma distribution with small shape parameter

Author

Listed:
  • Chuanhai Liu

    (Purdue University)

  • Ryan Martin

    (North Carolina State University)

  • Nick Syring

    (North Carolina State University)

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.

Suggested Citation

  • Chuanhai Liu & Ryan Martin & Nick Syring, 2017. "Efficient simulation from a gamma distribution with small shape parameter," Computational Statistics, Springer, vol. 32(4), pages 1767-1775, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0692-0
    DOI: 10.1007/s00180-016-0692-0
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    References listed on IDEAS

    as
    1. Kundu, Debasis & Gupta, Rameshwar D., 2007. "A convenient way of generating gamma random variables using generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2796-2802, March.
    2. repec:dau:papers:123456789/5724 is not listed on IDEAS
    3. Ryan Martin & Chuanhai Liu, 2015. "Marginal Inferential Models: Prior-Free Probabilistic Inference on Interest Parameters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1621-1631, December.
    4. Xi, Bowei & Tan, Kean Ming & Liu, Chuanhai, 2013. "Logarithmic Transformation-Based Gamma Random Number Generators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i04).
    5. Hisashi Tanizaki, 2008. "A Simple Gamma Random Number Generator for Arbitrary Shape Parameters," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-10.
    6. repec:ebl:ecbull:v:3:y:2008:i:7:p:1-10 is not listed on IDEAS
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    Cited by:

    1. Yu-Fang Chien & Haiming Zhou & Timothy Hanson & Theodore Lystig, 2023. "Informative g -Priors for Mixed Models," Stats, MDPI, vol. 6(1), pages 1-23, January.

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