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

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])