Module « scipy.special »

Fonction chdtr - module scipy.special

Signature de la fonction chdtr

Description

chdtr.__doc__

chdtr(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

chdtr(v, x, out=None)

Chi square cumulative distribution function.

Returns the area under the left tail (from 0 to `x`) of the Chi
square probability density function with `v` degrees of freedom:

.. math::

    \frac{1}{2^{v/2} \Gamma(v/2)} \int_0^x t^{v/2 - 1} e^{-t/2} dt

Here :math:`\Gamma` is the Gamma function; see `gamma`. This
integral can be expressed in terms of the regularized lower
incomplete gamma function `gammainc` as
``gammainc(v / 2, x / 2)``. [1]_

Parameters
----------
v : array_like
    Degrees of freedom.
x : array_like
    Upper bound of the integral.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    Values of the cumulative distribution function.

See Also
--------
chdtrc, chdtri, chdtriv, gammainc

References
----------
.. [1] Chi-Square distribution,
    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples
--------
>>> import scipy.special as sc

It can be expressed in terms of the regularized lower incomplete
gamma function.

>>> v = 1
>>> x = np.arange(4)
>>> sc.chdtr(v, x)
array([0.        , 0.68268949, 0.84270079, 0.91673548])
>>> sc.gammainc(v / 2, x / 2)
array([0.        , 0.68268949, 0.84270079, 0.91673548])