# Package com.numericalmethod.suanshu.analysis.function.special.gaussian

• Interface Summary
Interface Description
StandardCumulativeNormal
The cumulative Normal distribution function describes the probability of a Normal random variable falling in the interval $$(-\infty, x]$$.
• Class Summary
Class Description
CumulativeNormalHastings
Hastings algorithm is faster but less accurate way to compute the cumulative standard Normal.
CumulativeNormalInverse
The inverse of the cumulative standard Normal distribution function is defined as: $N^{-1}(u) /] This implementation uses the Beasley-Springer-Moro algorithm. CumulativeNormalMarsaglia Marsaglia is about 3 times slower but is more accurate to compute the cumulative standard Normal. Erf The Error function is defined as: \[ \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt$
Erfc
This complementary Error function is defined as: $\operatorname{erfc}(x) = 1-\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt$
ErfInverse
The inverse of the Error function is defined as: $\operatorname{erf}^{-1}(x)$
Gaussian
The Gaussian function is defined as: $f(x) = a e^{- { \frac{(x-b)^2 }{ 2 c^2} } }$