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(7 Feb 2013) Key: citeulike:12011229
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The gamma distribution with small shape parameter is difficult to characterize. In particular, standard algorithms for sampling from such a distribution often fail, so something special is needed. In this paper, we first 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. Pseudo-code, and an R implementation, for this new sampling algorithm are provided.
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