Draw samples from a noncentral chi-square distribution.
The noncentral
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distribution is a generalisation of
the
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distribution.
Parameters: | df : int
Degrees of freedom, should be >= 1.
nonc : float
Non-centrality, should be > 0.
size : int or tuple of ints
|
Notes
The probability density function for the noncentral Chi-square distribution
is
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where
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is the Chi-square with q degrees of freedom.
In Delhi (2007), it is noted that the noncentral chi-square is useful in
bombing and coverage problems, the probability of killing the point target
given by the noncentral chi-squared distribution.
References
[R153] | Delhi, M.S. Holla, “On a noncentral chi-square distribution in the
analysis of weapon systems effectiveness”, Metrika, Volume 15,
Number 1 / December, 1970. |
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, normed=True)
>>> plt.show()
(Source code, png, pdf)
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), normed=True)
>>> values2 = plt.hist(np.random.chisquare(3, 100000),
... bins=np.arange(0., 25, .1), normed=True)
>>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')
>>> plt.show()
(png, pdf)
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, normed=True)
>>> plt.show()
(png, pdf)