scipy.special.

ndtri#

scipy.special.ndtri(y, out=None)#

Inverse of ndtr vs x

Returns the argument x for which the area under the standard normal probability density function (integrated from minus infinity to x) is equal to y.

Parameters:

parray_like: Probability
outndarray, optional: Optional output array for the function results

Returns:

xscalar or ndarray: Value of x such that ndtr(x) == p.

See also

ndtr: Standard normal cumulative probability distribution
ndtri_exp: Inverse of log_ndtr

Notes

Array API Standard Support

ndtri has 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=1 and 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

ndtri is the percentile function of the standard normal distribution. This means it returns the inverse of the cumulative density ndtr. First, let us compute a cumulative density value.

>>> importnumpyasnp
>>> fromscipy.specialimport ndtri, ndtr
>>> cdf_val = ndtr(2)
>>> cdf_val
0.9772498680518208

Verify that ndtri yields the original value for x up to floating point errors.

>>> ndtri(cdf_val)
2.0000000000000004

Plot the function. For that purpose, we provide a NumPy array as argument.

>>> importmatplotlib.pyplotasplt
>>> x = np.linspace(0.01, 1, 200)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, ndtri(x))
>>> ax.set_title("Standard normal percentile function")
>>> plt.show()

../../_images/scipy-special-ndtri-1.png