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 functiongammaincc
asgammaincc(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.
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 variableSCIPY_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])