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

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 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])