Simulating from a gamma distribution with small shape parameter

2013/02/07 by Chuanhai Liu, Liu, Chuanhai, Ryan Martin +2
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1302.1884

openalex publication_date 2013/02/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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