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

log of the standard normal cumulative distribution function

ndtr

standard normal cumulative distribution function

ndtri

standard normal percentile function

Examples

>>> import numpy as np
>>> 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
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