Error function

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

The definition is

erf⁡(x)=2π∫0xexp⁡(−t2)dt.

The complementary error function is defined as

erfc⁡(x)=1−erf⁡(x).

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

F(x;μ,σ)=12[1+erf⁡(x−μσ2)].