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arXiv · 2604.11199

Extended One-Liners for the Beta, Gamma, and Dirichlet Distributions with Shape Parameters Below One

Dylan Greaves
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Abstract

We present an explicit deterministic transformation of a fixed number of i.i.d. uniform random variables with exact Beta$(a,1-a)$ law for $0<a<1$, using only elementary operations (an ``extended one-liner'', see \cite{devroye1996oneline}). As corollaries, the families Beta$(a,b)$ with $\min(a,b)<1$, Gamma$(c)$ with $c<1$, and Dirichlet$(\alpha_1,\dots,\alpha_d)$ with $0<\alpha_i<1$, for fixed $d$, also have extended one-\liners.

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Dylan Greaves. 2026-04-13. Extended One-Liners for the Beta, Gamma, and Dirichlet Distributions with Shape Parameters Below One. https://arxiv.org/abs/2604.11199

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