numpy.random.noncentral_chisquare
-
numpy.random.noncentral_chisquare(df, nonc, size=None)
-
Draw samples from a noncentral chi-square distribution.
The noncentral
distribution is a generalization of the
distribution.
Note
New code should use the
noncentral_chisquare
method of adefault_rng()
instance instead; seerandom-quick-start
.- Parameters
-
-
dffloat or array_like of floats
-
Degrees of freedom, must be > 0.
Changed in version 1.10.0: Earlier NumPy versions required dfnum > 1.
-
noncfloat or array_like of floats
-
Non-centrality, must be non-negative.
-
sizeint or tuple of ints, optional
-
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifdf
andnonc
are both scalars. Otherwise,np.broadcast(df, nonc).size
samples are drawn.
-
- Returns
-
-
outndarray or scalar
-
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
where
is the Chi-square with q degrees of freedom.
References
-
1
-
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()
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Licensed under the 3-clause BSD License.
https://numpy.org/doc/1.18/reference/random/generated/numpy.random.noncentral_chisquare.html