`numpy.random._generator:Generator.noncentral_chisquare`

Signature

def noncentral_chisquare(df, nonc, size = None)

Summary

Draw samples from a noncentral chi-square distribution.

Extended Summary

The noncentral $χ^{2}$ distribution is a generalization of the $χ^{2}$ distribution.

Parameters

df : float or array_like of floats: Degrees of freedom, must be > 0.
nonc : float or array_like of floats: Non-centrality, must be non-negative.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if df and nonc are both scalars. Otherwise, np.broadcast(df, nonc).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized noncentral chi-square distribution.

Notes

The probability density function for the noncentral Chi-square distribution is

P (x; df, n o n c) = i = 0 \sum \infty \frac{e ^{- n o n c /2} ( n o n c /2 ) ^{i}}{i !} P_{Y_{df + 2 i}} (x),

where $Y_{q}$ is the Chi-square with q degrees of freedom.

Examples

Draw values from the distribution and plot the histogram

rng = np.random.default_rng()
import matplotlib.pyplot as plt
values = plt.hist(rng.noncentral_chisquare(3, 20, 100000),
                  bins=200, density=True)
plt.show()

✓

Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare.

plt.figure()

✗

<Figure size 640x480 with 0 Axes>

values = plt.hist(rng.noncentral_chisquare(3, .0000001, 100000),
                  bins=np.arange(0., 25, .1), density=True)
values2 = plt.hist(rng.chisquare(3, 100000),
                   bins=np.arange(0., 25, .1), density=True)

✓

plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')

✗

[<matplotlib.lines.Line2D object at 0x7f2206e5fa10>]

plt.show()

✓

Demonstrate how large values of non-centrality lead to a more symmetric distribution.

plt.figure()

✗

<Figure size 640x480 with 0 Axes>

values = plt.hist(rng.noncentral_chisquare(3, 20, 100000),
                  bins=200, density=True)
plt.show()

✓