File:Generalized inversion method.svg

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English: F(x)=Pr{X≤x} is a cumulative distribution function of random variable X. U is a random variable uniformly distributed on [0,1]. In general, y=F(x) (0≤y≤1) does not necessarily have inverse function F-1(y). However, we can define the inverse function by F-1(y)=inf{x|F(x)≥y} since F(x) is non-decreasing and right-continuous. Thus, we can take F-1(y) in the inversion method. F-1(U) has the same distribution as X.
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Author Ta2o

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Schematic of generalized inversion method for random variate generation

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23 June 2019

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current03:09, 23 June 2019Thumbnail for version as of 03:09, 23 June 2019630 × 630 (69 KB)Ta2oUser created page with UploadWizard
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