Probability integral transform

In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, the probability integral transform (also known as universality of the uniform) relates to the result that data values that are modeled as being <a href="/facts/Random_variable/TwTBXnLT">random variables</a> from any given <a href="/facts/Continuous_distribution/EpsKKVRu">continuous distribution</a> can be converted to random variables having a <a href="/facts/Continuous_uniform_distribution/XbnlVljT">standard uniform distribution</a>. This holds exactly provided that the distribution being used is the true distribution of the random variables; if the distribution is one <a href="/facts/Curve_fitting/zrLKw6Xj">fitted to the data</a>, the result will hold approximately in large samples.
The result is sometimes modified or extended so that the result of the transformation is a standard distribution other than the uniform distribution, such as the <a href="/facts/Exponential_distribution/yY3EdV0u">exponential distribution</a>.
The transform was introduced by <a href="/facts/Ronald_Fisher/I2FVIpy9">Ronald Fisher</a> in his 1932 edition of the book <a href="/facts/Statistical_Methods_for_Research_Workers/aRppN873">Statistical Methods for Research Workers</a>.

Probability integral transform open-in-new

Probability integral transform