Inverse transform sampling: Difference between revisions

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Revision as of 22:41, 3 October 2006

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==Proof of correctness==

Let ''F'' be a continuous [[cumulative distribution function]], and let <math>F^{-1}</math> be its inverse function:<ref>Luc Devroye. ''Non-Uniform Random Variate Generation''. New York: Springer-Verlag, 1986. ([http://cgmcg.csscs.mcgillcarleton.ca/~luc/rnbookindex.html online]) ''See [http://cgmcg.csscs.mcgillcarleton.ca/~luc/chapter_twohandbooksimulation1.pdf chapter 2], section 2, p. 28.''</ref>

:<math>F^{-1}(u) = \inf\;\{x \mid F(x)=u, 0<u<1\}</math>