The error function erf(x),
usually normalized to one with a factor 2/√π, is the integral
of the Gauss curve. It is also called the integrated Gauss function or the integrated distribution. The function
gives the probability that a measurement under the influence of accidental errors has a
distance less than x from the average value at the center.
The inverse error function is used in computing confidence intervals in statistics and in some algorithms for generating Gaussian random numbers.