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