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# 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`

  Notes

  `chdtrc` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  See Support for the array API standard for more information.

  References

  [1]

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

  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])