Inverse transform sampling: Difference between revisions

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The '''inverse transform sampling method''' is a method of sampling a number at random from any [[probability distribution]] given its [[cumulative distribution function]] (cdf).

random from any [[probability distribution]], given its [[cumulative distribution function]] (cdf).

==The method==

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The problem that the inverse transform sampling method solves is as follows:

*Let ''X'' be a [[random variable]] whose distribution can be described by the cdf d(''xF'').

*We want to generate values of ''xX'' which are distributed according to this distribution.

Many [[programming language]]s have the ability to generate [[pseudorandom number sequence|pseudo-random numbers]] which are effectively distributed according to the standard [[uniform distribution]]. If a random variable has that distribution, then the probability of its falling within any subinterval (''a'', ''b'') of the interval from 0 to 1 is just the length ''b'' -− ''a'' of that subinterval.

The inverse transform sampling method works as follows:

#Generate a random number from the standard uniform distribution; call this ''u''.

#Compute the value for ''x'' whichsuch hasthat the<math>F(x) associated= cdf value ''u''</math>; call this ''x''_''chosen''.

#Take ''x''_''chosen'' to be the random number drawn from the distribution described by d(''xF'').

==Proof of correctness==