Draw samples from a noncentral chi-square distribution.
The noncentral
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distribution is a generalization of
the
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distribution.
Note
New code should use the noncentral_chisquare
method of a default_rng()
instance instead; see random-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)
, 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
- outndarray or scalar
Drawn samples from the parameterized noncentral chi-square distribution.
Notes
The probability density function for the noncentral Chi-square
distribution is
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\frac{e^{-nonc/2}(nonc/2)^{i}}{i!}
P_{Y_{df+2i}}(x),
)
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where
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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()