scipy.special.chndtr#

scipy.special.chndtr(x, df, nc, out=None) = <ufunc 'chndtr'>#

Non-central chi square cumulative distribution function

The cumulative distribution function is given by:

\[P(\chi^{\prime 2} \vert \nu, \lambda) =\sum_{j=0}^{\infty} e^{-\lambda /2} \frac{(\lambda /2)^j}{j!} P(\chi^{\prime 2} \vert \nu + 2j),\]

where \(\nu > 0\) is the degrees of freedom (df) and \(\lambda \geq 0\) is the non-centrality parameter (nc).

Parameters:
xarray_like

Upper bound of the integral; must satisfy x >= 0

dfarray_like

Degrees of freedom; must satisfy df > 0

ncarray_like

Non-centrality parameter; must satisfy nc >= 0

outndarray, optional

Optional output array for the function results

Returns:
xscalar or ndarray

Value of the non-central chi square cumulative distribution function.

See also

chndtrix

Noncentral Chi Squared distribution quantile

chndtridf

Inverse of chndtr with respect to df

chndtrinc

Inverse of chndtr with respect to nc

scipy.stats.ncx2

Non-central chi-squared distribution

Notes

The noncentral chi squared distribution is also available in scipy.stats.ncx2. scipy.stats.ncx2.cdf is equivalent to chndtr.

This function wraps routines from the Boost Math C++ library [1].

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

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

Compute the noncentral chi squared distribution CDF at one point.

>>> x = 4.0
>>> df = 1.0
>>> nc = 5.0
>>> sc.chndtr(x, df, nc)
0.40667858759710945

Plot the noncentral chi squared distribution CDF for different parameters.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0, 40, 1000)
>>> plt.plot(x, sc.chndtr(x, 1, 5), label=r"$df=1,\ nc=5$")
>>> plt.plot(x, sc.chndtr(x, 5, 10), label=r"$df=5,\ nc=10$")
>>> plt.legend()
>>> plt.show()
../../_images/scipy-special-chndtr-1.png