| Interface | Description |
|---|---|
| StandardCumulativeNormal |
The cumulative Normal distribution function describes the probability of a Normal random variable falling in the interval \((-\infty, x]\).
|
| 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:
\[
f(x) = a e^{- { \frac{(x-b)^2 }{ 2 c^2} } }
\]
|