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inverse transformation method

Source:
A Dictionary of Statistics

inverse transformation method 

A general method for the simulation of observations of a continuous random variable X.

Let u be a pseudo-random number and let F be the distribution function of X. Then x, given by

x=F1(u),
is a random observation of X. For example, an exponential random variable X, with mean μ, has distribution function (1 − ex/μ); hence − μ ln (1−u) is an observation of X.