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The probit function is the quantile function of the standard normal distribution. For a probability , it is given by

where is the cumulative distribution function of the standard normal distribution and is the inverse erf function. In the convention of Bliss (1934), the same quantile is shifted by 5, so that a probability of 1/2 corresponds to 5.

The probit function serves as a link for binary responses in a generalized linear model. With this link, the response probability is , where is the linear predictor.

The probit function will be implemented in a future version of the Wolfram Language as Probit[p].

See also

Generalized Linear Model, Inverse Erf, Logit Function, Quantile Function, Standard Normal Distribution

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References

Bliss, C. I. "The Method of Probits--A Correction." Science 79, 409-410, 1934. https://doi.org/10.1126/science.79.2053.409.

Cite this as:

Weisstein, Eric W. "Probit Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProbitFunction.html

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