Inverse transform sampling: Difference between revisions

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'''Inverse transform sampling''' (also known as '''inversion sampling''', the '''inverse probability integral transform''', the '''inverse transformation method''', '''[[Nikolai Smirnov (mathematician)|Smirnov]] transform''', '''universality of the uniform''', or the '''golden rule'''<ref name=aalto>Aalto University, N. Hyvönen, Computational methods in inverse problems. Twelfth lecture https://noppa.tkk.fi/noppa/kurssi/mat-1.3626/luennot/Mat-1_3626_lecture12.pdf{{dead link|date=November 2017 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>) is a basic method for [[pseudo-random number sampling]], i.e., for generating sample numbers at [[random]] from any [[probability distribution]] given its [[cumulative distribution function]].

Inverse transformation sampling takes [[Continuous uniform distribution|uniform samples]] of a number <math>u</math> between 0 and 1, interpreted as a probability, and then returns the largest number <math>x</math> from the ___domain of the distribution <math>P(X)</math> such that <math>P(-\infty < X < x) \le u</math>. For example, imagine that <math>P(X)</math> is the standard [[normal distribution]] with mean zero and standard deviation one. The table below shows samples taken from the uniform distribution and their representation on the standard normal distribution.