jax.scipy.special.ndtr

jax.scipy.special.ndtr(x)

Normal distribution function.

Returns the area under the Gaussian probability density function, integrated from minus infinity to x:

\[\begin{split}\begin{align} \mathrm{ndtr}(x) =& \ \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{x} e^{-\frac{1}{2}t^2} dt \\ =&\ \frac{1}{2} (1 + \mathrm{erf}(\frac{x}{\sqrt{2}})) \\ =&\ \frac{1}{2} \mathrm{erfc}(\frac{x}{\sqrt{2}}) \end{align}\end{split}\]

Parameters:

x (Union[Array, ndarray, bool_, number, bool, int, float, complex]) – An array of type float32, float64.

Return type:

Array

Returns:

An array with dtype=x.dtype.

Raises:

TypeError – if x is not floating-type.