# 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). 

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.

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])


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