Probit - Computation

Computation

The normal distribution CDF and its inverse are not available in closed form, and computation requires careful use of numerical procedures. However, the functions are widely available in software for statistics and probability modeling, and in spreadsheets. In Microsoft Excel, for example, the probit function is available as normsinv(p). In computing environments where numerical implementations of the inverse error function are available, the probit function may be obtained as

\operatorname{probit}(p) = \sqrt{2}\,\operatorname{erf}^{-1}(2p-1).

An example is MATLAB, where an 'erfinv' function is available. The language Mathematica implements 'InverseErf'. Other environments directly implement the probit function as is shown in the following session in the R programming language.

> qnorm(0.025) -1.959964 > pnorm(-1.96) 0.02499790

Details for computing the inverse error function can be found at . Wichura gives a fast algorithm for computing the probit function to 16 decimal places; this is used in R to generate random variates for the normal distribution.

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