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- gammaincas- 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. 
 
 - Notes - chdtrhas 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=1and 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 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])