We wish to sample from the pdf [ f(x)=x mathrm{e}^{-x}, quad x geqslant 0 ] using acceptance-rejection

Question:

We wish to sample from the pdf

\[ f(x)=x \mathrm{e}^{-x}, \quad x \geqslant 0 \]

using acceptance-rejection with the proposal pdf $g(x)=e^{-x / 2} / 2, x \geqslant 0$.

(a) Find the smallest $C$ for which $C g(x) \geqslant f(x)$ for all $x$.

(b) What is the efficiency of this acceptance-rejection method?

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Data Science And Machine Learning Mathematical And Statistical Methods

ISBN: 9781118710852

1st Edition

Authors: Dirk P. Kroese, Thomas Taimre, Radislav Vaisman, Zdravko Botev

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Question Posted: May 19, 2024 02:03 AM

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We wish to sample from the pdf [ f(x)=x mathrm{e}^{-x}, quad x geqslant 0 ] using acceptance-rejection

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Data Science And Machine Learning Mathematical And Statistical Methods

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