A simple method for generating gamma variables

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SHOPPER: A Probabilistic Model of Consumer Choice with Substitutes and Complements (2017, methodology): “For a gamma variational factor with shape α and mean μ, we use the transformation based on rejection sampling (Marsaglia and Tang, 2000),”
Augur: Data-Parallel Probabilistic Modeling (2014, unknown): “As an example, to draw θm as part of the (τ + 1)th sample, the compiler needs to generate code that samples from the following distribution p(θτ+1m | wτ+1, zτ+1, θτ+11 , ..., θ τ+1 m−1, θ τ m+1, ..., θ τ M ).”
WHAI: Weibull Hybrid Autoencoding Inference for Deep Topic Modeling (2018, unknown): “More specifically, following Naesseth et al., to generate a gamma random variable z ∼ Gamma(α, β), one may first use the rejection sampler of Marsaglia & Tsang (2000) to generate z̃ ∼ Gamma(α+B, 1), for which the proposal distribution is expressed as z̃ = ( α+B − 1 3 )( 1 + ε√ 9(α+B)− 3 )3 , ε ∼ N…”
TensorFlow Distributions (2017, methodology): “Draws from Gamma use the rejection sampling algorithm of Marsaglia and Tsang [30]; currently, only a CPU implementation exists.”
The Amoroso Distribution (2010, methodology): “Therefore, Amoroso random numbers can be obtained by sampling from the standard gamma distribution, for instance using the Marsaglia-Tsang fast gamma method [29] and applying the appropriate transformation [26].”