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3.2.4 Rejection Method

A classic: created by John von Neumann, applicable to almost any $p(x)$.

Here is the original formulation:

             

And this is how we read it today:

\fbox{\begin{minipage}{600pt} {\bf Rejection method:} \\ [12pt] Let $[a,b]$\ be... ...xt random number, otherwise return to step 1.} \end{enumerate}\end{minipage} }

\begin{figure}\includegraphics[height=180pt]{figures/f3rej2.ps} \end{figure}
The method is simple and fast, but it becomes inefficient whenever the area of the rectangle $[a,b]\otimes [0,p_{m}]$ is large compared to the area below the graph of $p(x)$. Otherwise, the ``Improved Rejection Method'' may be applicable: $\Longrightarrow$

\fbox{\begin{minipage}{600pt} {\bf Improved rejection method:}\\ [12pt] Let $f(... ...the next random number, else return to Step 1.} \end{enumerate}\end{minipage} }
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001