scipy.special.chdtr#

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

Chi square cumulative distribution function.

Returns the area under the left tail (from 0 to x) of the Chi square probability density function with v degrees of freedom:

\[\frac{1}{2^{v/2} \Gamma(v/2)} \int_0^x t^{v/2 - 1} e^{-t/2} dt\]

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

Parameters:
varray_like

Degrees of freedom.

xarray_like

Upper bound of the integral.

outndarray, optional

Optional output array for the function results.

Returns:
scalar or ndarray

Values of the cumulative distribution function.

See also

chdtrc, chdtri, chdtriv, gammainc

Notes

chdtr 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

Examples

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

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

>>> v = 1
>>> x = np.arange(4)
>>> sc.chdtr(v, x)
array([0.        , 0.68268949, 0.84270079, 0.91673548])
>>> sc.gammainc(v / 2, x / 2)
array([0.        , 0.68268949, 0.84270079, 0.91673548])
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