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].
