jax.scipy.special.ndtr

jax.scipy.special.ndtr(x)[source]

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 – An array of type float32, float64.

Returns

An array with dtype=x.dtype.

Raises

TypeError – if x is not floating-type.