world:ratio-of-uniform
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world:ratio-of-uniform [2023/04/20 08:55] rdouc |
world:ratio-of-uniform [2023/04/20 08:57] (current) rdouc [The idea] |
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| - | ====== The idea ====== | + | ====== The ratio of uniform method ====== |
| The rejection algorithm is based on the following property: | The rejection algorithm is based on the following property: | ||
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| A simple generalisation of this result is: if $ (U,V) \sim \unif\set{(u,v)}{0\leq u\leq G^{-1}\lr{M f\lr{\frac { v} {g(u)}}}}$, then $V/g(U) \sim f$ where $g: \rset^+ \to \rset^+_*$ and $G(x)=\int_0^x g(u) \rmd u$. | A simple generalisation of this result is: if $ (U,V) \sim \unif\set{(u,v)}{0\leq u\leq G^{-1}\lr{M f\lr{\frac { v} {g(u)}}}}$, then $V/g(U) \sim f$ where $g: \rset^+ \to \rset^+_*$ and $G(x)=\int_0^x g(u) \rmd u$. | ||
| - | As far as I can see, these methods can only be interesting if $V=Y g(X)$ or $U=X$ are easy to simulate when $Y \sim f$ and $X|_Y \sim \unif\lrcb{[0,f(Y)]}$ | + | As far as I can see, these methods can only be interesting if $V=Y g(X)$ or $U=X$ are easy to simulate when $Y \sim f$ and $X|_Y \sim \unif\lrcb{[0,f(Y)]}$. This is very linked to rejection algorithm... |
| * [[https://dl.acm.org/doi/pdf/10.1145/355744.355750|ratio-of-uniform method]] | * [[https://dl.acm.org/doi/pdf/10.1145/355744.355750|ratio-of-uniform method]] | ||
| * {{ :mynotes:bf01889987.pdf | Generalisation of the ratio-of-uniform method}} | * {{ :mynotes:bf01889987.pdf | Generalisation of the ratio-of-uniform method}} | ||
world/ratio-of-uniform.1681973721.txt.gz · Last modified: 2023/04/20 08:55 by rdouc
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