Inverse transform sampling: Difference between revisions

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Importing Wikidata short description: "Basic method for pseudo-random number sampling" (Shortdesc helper)
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Expressed differently, given a continuous uniform variable <math>U</math> in <math>[0,1]</math> and an [[Inverse function|invertible]] cumulative distribution function <math>F_X</math>, the random variable <math>X = F_X^{-1}(U)</math> has distribution <math>F_X</math> (or, <math>X</math> is distributed <math>F_X</math>).
 
A treatment of such inverse functions as objects satisfying differential equations can be given.<ref>{{cite journal | last1 = Steinbrecher, G.,| first1 = György | last2 = Shaw, W.| first2 = William T. (2008).| title = Quantile mechanics. ''| journal = European Journal of Applied Mathematics'' | date = 19 (March 2008 | volume = 19 | issue = 2): 87–112| doi = 10.1017/S0956792508007341}}</ref> Some such differential equations admit explicit power series solutions, despite their non-linearity.{{Citation needed|date=July 2017}}
 
== Examples ==