scipy.special.ndtr#
- 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 
 
 - See also - log_ndtr
- Logarithm of ndtr 
- ndtri
- Inverse of ndtr, standard normal percentile function 
- erf
- Error function 
- erfc
- 1 - erf 
- scipy.stats.norm
- Normal distribution 
 - Notes - ndtrhas experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable- SCIPY_ARRAY_API=1and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.- Library - CPU - GPU - NumPy - ✅ - n/a - CuPy - n/a - ✅ - PyTorch - ✅ - ✅ - JAX - ✅ - ✅ - Dask - ✅ - n/a - See Support for the array API standard for more information. - Examples - Evaluate - ndtrat 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 $\Phi$") >>> plt.show() 