Probit

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In probability theory and statistics the probit function is the inverse cumulative distribution function, or quantile function of the normal distribution.

The probit function is often denoted as $Φ - 1$ and is of type:

$\Phi^{-1}: [0;1] \to (-\infty;+\infty) \!$

Plot of probit function

Like the logit (log odds) function, it may be used to transform a variable $p$ ranging over the interval $[0,1]$ into a derived quantity $Φ - 1 (p)$ ranging over the real numbers. This has applications in probit models, which are generalized linear models.

The probit function may be expressed in terms of the inverse of the error function:

$\Phi^{-1}(p)=\sqrt{2}\,\operatorname{erf}^{-1}(2p-1)$