scipy.special.chdtrc#

scipy.special.chdtrc(v, x, out=None) = <ufunc 'chdtrc'>#

Chi square survival function.

Returns the area under the right hand tail (from x to infinity) of the Chi square probability density function with v degrees of freedom:

\[\frac{1}{2^{v/2} \Gamma(v/2)} \int_x^\infty t^{v/2 - 1} e^{-t/2} dt\]

Here \(\Gamma\) is the Gamma function; see gamma. This integral can be expressed in terms of the regularized upper incomplete gamma function gammaincc as gammaincc(v / 2, x / 2). [1]

Parameters:
varray_like

Degrees of freedom.

xarray_like

Lower bound of the integral.

outndarray, optional

Optional output array for the function results.

Returns:
scalar or ndarray

Values of the survival function.

See also

chdtr, chdtri, chdtriv, gammaincc

References

Examples

>>> import numpy as np
>>> import scipy.special as sc

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

>>> v = 1
>>> x = np.arange(4)
>>> sc.chdtrc(v, x)
array([1.        , 0.31731051, 0.15729921, 0.08326452])
>>> sc.gammaincc(v / 2, x / 2)
array([1.        , 0.31731051, 0.15729921, 0.08326452])