High Quality Content by WIKIPEDIA articles! Inverse transform sampling, also known as the inverse probability integral transform or inverse transformation method or Smirnov transform, is a method for generating sample numbers at random from any probability distribution given its cumulative distribution function (cdf). Subject to the restriction that the distribution is continuous, this method is generally applicable (and can be computationally efficient if the cdf can be analytically inverted), but may be too computationally expensive in practice for some probability distributions. The Box-Muller transform is an example of an algorithm that is specific to generating samples from a normal distribution, but is more computationally efficient. It is often the case that, even for simple distributions, the inverse transform sampling method can be improved on: see, for example, the ziggurat algorithm and rejection sampling.

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