scipy.special.ndtr — SciPy v1.15.2 Manual (original) (raw)

scipy.special.ndtr(x, out=None) = <ufunc 'ndtr'>#

Cumulative distribution of the standard normal distribution.

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

\[\frac{1}{\sqrt{2\pi}} \int_{-\infty}^x \exp(-t^2/2) dt\]

Parameters:

xarray_like, real or complex

Argument

outndarray, optional

Optional output array for the function results

Returns:

scalar or ndarray

The value of the normal CDF evaluated at x

Examples

Evaluate ndtr at one point.

import numpy as np from scipy.special import ndtr ndtr(0.5) 0.6914624612740131

Evaluate the function at several points by providing a NumPy array or list for x.

ndtr([0, 0.5, 2]) array([0.5 , 0.69146246, 0.97724987])

Plot the function.

import matplotlib.pyplot as plt x = np.linspace(-5, 5, 100) fig, ax = plt.subplots() ax.plot(x, ndtr(x)) ax.set_title(r"Standard normal cumulative distribution function Φ\PhiΦ") plt.show()