Inverse transform sampling: Difference between revisions

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==Proof of correctness==

Let ''F'' be a continuous [[cumulative distribution function]], and let ''F''^&minus;1 be its [https://en.wikipedia.org/wiki/Cumulative_distribution_function#Inverse_distribution_function_(quantile_function) generalized inverse function] (using the [[infimum]] because CDFs are weakly monotonic and [[Càdlàg|right-continuous]]):<ref>{{cite book |author=Luc Devroye |title=Non-Uniform Random Variate Generation |publisher=Springer-Verlag |place=New York |year=1986 |chapter=Section 2.2. Inversion by numerical solution of ''F''(''X'')&nbsp;=&nbsp;''U'' |chapter-url=http://luc.devroye.org/chapter_two.pdf}}</ref>

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