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Module « scipy.special »

Fonction log_ndtr - module scipy.special

Signature de la fonction log_ndtr

def log_ndtr(*args, **kwargs) 

Description

help(scipy.special.log_ndtr)

log_ndtr(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

log_ndtr(x, out=None)

Logarithm of Gaussian cumulative distribution function.

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

    log(1/sqrt(2*pi) * integral(exp(-t**2 / 2), t=-inf..x))

Parameters
----------
x : array_like, real or complex
    Argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The value of the log of the normal CDF evaluated at `x`

See Also
--------
erf
erfc
scipy.stats.norm
ndtr

Examples
--------
>>> import numpy as np
>>> from scipy.special import log_ndtr, ndtr

The benefit of ``log_ndtr(x)`` over the naive implementation
``np.log(ndtr(x))`` is most evident with moderate to large positive
values of ``x``:

>>> x = np.array([6, 7, 9, 12, 15, 25])
>>> log_ndtr(x)
array([-9.86587646e-010, -1.27981254e-012, -1.12858841e-019,
       -1.77648211e-033, -3.67096620e-051, -3.05669671e-138])

The results of the naive calculation for the moderate ``x`` values
have only 5 or 6 correct significant digits. For values of ``x``
greater than approximately 8.3, the naive expression returns 0:

>>> np.log(ndtr(x))
array([-9.86587701e-10, -1.27986510e-12,  0.00000000e+00,
        0.00000000e+00,  0.00000000e+00,  0.00000000e+00])

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