numpy.random.
noncentral_chisquare
Draw samples from a noncentral chi-square distribution.
The noncentral
System Message: WARNING/2 (\chi^2)
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Note
New code should use the noncentral_chisquare method of a default_rng() instance instead; see random-quick-start.
default_rng()
Degrees of freedom, must be > 0.
Changed in version 1.10.0: Earlier NumPy versions required dfnum > 1.
Non-centrality, must be non-negative.
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.
(m, n, k)
m * n * k
None
df
nonc
np.broadcast(df, nonc).size
Drawn samples from the parameterized noncentral chi-square distribution.
See also
Generator.noncentral_chisquare
which should be used for new code.
Notes
The probability density function for the noncentral Chi-square distribution is
System Message: WARNING/2 (P(x;df,nonc) = \sum^{\infty}_{i=0} \frac{e^{-nonc/2}(nonc/2)^{i}}{i!} P_{Y_{df+2i}}(x), )
where
System Message: WARNING/2 (Y_{q})
References
Wikipedia, “Noncentral chi-squared distribution” https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
Examples
Draw values from the distribution and plot the histogram
>>> import matplotlib.pyplot as plt >>> values = plt.hist(np.random.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() >>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000), ... bins=np.arange(0., 25, .1), density=True) >>> values2 = plt.hist(np.random.chisquare(3, 100000), ... bins=np.arange(0., 25, .1), density=True) >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob') >>> plt.show()
Demonstrate how large values of non-centrality lead to a more symmetric distribution.
>>> plt.figure() >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000), ... bins=200, density=True) >>> plt.show()
