Dictionary:Error function

The error function erf(t) is

${\text{erf}}(t)={\frac {2}{\sqrt {\pi }}}\int _{0}^{x}e^{-y^{2}}dy$

Note

${\text{erf}}(0)=0,\;{\text{erf}}(\infty )=1.$

The complementary error function erfc(t) is

${\text{erfc}}(t)=1-{\text{erf}}(t)$.

For data which have a Gaussian distribution, the probability that an error lies between ±a is erf(ha), where h=precision index.