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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2604.11199 |
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| _version_ | 1866914468977442816 |
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| author | Greaves, Dylan |
| author_facet | Greaves, Dylan |
| contents | 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$(α_1,\dots,α_d)$ with $0<α_i<1$, for fixed $d$, also have extended one-\liners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extended One-Liners for the Beta, Gamma, and Dirichlet Distributions with Shape Parameters Below One Greaves, Dylan Computation Probability 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$(α_1,\dots,α_d)$ with $0<α_i<1$, for fixed $d$, also have extended one-\liners. |
| title | Extended One-Liners for the Beta, Gamma, and Dirichlet Distributions with Shape Parameters Below One |
| topic | Computation Probability |
| url | https://arxiv.org/abs/2604.11199 |