Editing Rejection sampling (section)

==Algorithm==
The algorithm, which was used by [[John von Neumann]]<ref>{{Cite journal |last=Forsythe |first=George E. |date=1972 |title=Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions |url=https://www.jstor.org/stable/2005864 |journal=Mathematics of Computation |volume=26 |issue=120 |pages=817–826 |doi=10.2307/2005864 |jstor=2005864 |issn=0025-5718}}</ref> and dates back to [[Georges-Louis Leclerc, Comte de Buffon|Buffon]] and [[Buffon's needle|his needle]],<ref>{{Cite journal |last1=Legault |first1=Geoffrey |last2=Melbourne |first2=Brett A. |date=2019-03-01 |title=Accounting for environmental change in continuous-time stochastic population models |url=https://doi.org/10.1007/s12080-018-0386-z |journal=Theoretical Ecology |language=en |volume=12 |issue=1 |pages=31–48 |doi=10.1007/s12080-018-0386-z |issn=1874-1746}}</ref> obtains a sample from distribution <math>X</math> with density <math>f</math> using samples from distribution <math>Y</math> with density <math>g</math> as follows:
* Obtain a sample <math>y</math> from distribution <math>Y</math> and a sample <math>u</math> from <math>\mathrm{Unif}(0,1)</math> (the uniform distribution over the unit interval).
* Check if <math display="inline">u<f(y)/Mg(y)</math>.
** If this holds, accept <math>y</math> as a sample drawn from <math>f</math>;
** if not, reject the value of <math>y</math> and return to the sampling step.

The algorithm will take an average of <math>M</math> iterations to obtain a sample.<ref>{{Cite book |last=Thomopoulos |first=Nick T. |title=Essentials of Monte Carlo Simulation: Statistical Methods for Building Simulation Models |date=2012-12-19 |publisher=Springer |isbn=978-1-4614-6021-3 |edition=2013th |location=New York, NY Heidelberg |language=English}}</ref>