Error function

In mathematics, the error function is a function associated with the cumulative distribution function of the normal distribution.

The definition is


 * $$\operatorname{erf}(x) = \frac{2}{\sqrt\pi} \int_{0}^{x} \exp(-t^2) dt .\,$$

The probability that a normally distributed random variable X with mean μ and variance σ2 exceeds x is


 * $$F(x;\mu,\sigma)=\frac{1}{2} \left[ 1 + \operatorname{erf} \left( \frac{x-\mu}{\sigma\sqrt{2}} \right) \right].

$$