# 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.

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 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])

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