-
RandomState.noncentral_chisquare(df, nonc, size=None)
-
Draw samples from a noncentral chi-square distribution.
The noncentral distribution is a generalisation of the distribution.
Parameters: df : int
Degrees of freedom, should be > 0 as of Numpy 1.10, should be > 1 for earlier versions.
nonc : float
Non-centrality, should be non-negative.
size : int or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. Default is None, in which case a single value is returned.Notes
The probability density function for the noncentral Chi-square distribution is
where 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
[R174] Delhi, M.S. Holla, ?On a noncentral chi-square distribution in the analysis of weapon systems effectiveness?, Metrika, Volume 15, Number 1 / December, 1970. [R175] Wikipedia, ?Noncentral chi-square distribution? http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution Examples
Draw values from the distribution and plot the histogram
1234>>>
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.
1234567>>> 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.
1234>>> plt.figure()
>>> values
=
plt.hist(np.random.noncentral_chisquare(
3
,
20
,
100000
),
... bins
=
200
, normed
=
True
)
>>> plt.show()
(png, pdf)
RandomState.noncentral_chisquare()
2017-01-10 18:19:40
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