scipy.special.chdtr¶
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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 functiongammaincasgammainc(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.
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])