scipy.special.ndtri_exp

scipy.special.ndtri_exp(y, out=None) = <ufunc 'ndtri_exp'>

Inverse of log_ndtr vs x. Allows for greater precision than ndtri composed with numpy.exp for very small values of y and for y close to 0.

Parameters

yarray_like of float

Function argument

outndarray, optional

Optional output array for the function results

Returns

scalar or ndarray

Inverse of the log CDF of the standard normal distribution, evaluated at y.

See also

log_ndtr, ndtri, ndtr

Examples

>>> import scipy.special as sc

ndtri_exp agrees with the naive implementation when the latter does not suffer from underflow.

>>> sc.ndtri_exp(-1)
-0.33747496376420244
>>> sc.ndtri(np.exp(-1))
-0.33747496376420244

For extreme values of y, the naive approach fails

>>> sc.ndtri(np.exp(-800))
-inf
>>> sc.ndtri(np.exp(-1e-20))
inf

whereas ndtri_exp is still able to compute the result to high precision.

>>> sc.ndtri_exp(-800)
-39.88469483825668
>>> sc.ndtri_exp(-1e-20)
9.262340089798409