mars.tensor.random.noncentral_chisquare¶
- mars.tensor.random.noncentral_chisquare(df, nonc, size=None, chunk_size=None, gpu=None, dtype=None)[源代码]¶
Draw samples from a noncentral chi-square distribution.
The noncentral \(\chi^2\) distribution is a generalisation of the \(\chi^2\) distribution.
- 参数
df (float or array_like of floats) – Degrees of freedom, should be > 0.
nonc (float or array_like of floats) – 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. If size isNone
(default), a single value is returned ifdf
andnonc
are both scalars. Otherwise,mt.broadcast(df, nonc).size
samples are drawn.chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension
gpu (bool, optional) – Allocate the tensor on GPU if True, False as default
dtype (data-type, optional) – Data-type of the returned tensor.
- 返回
out – Drawn samples from the parameterized noncentral chi-square distribution.
- 返回类型
Tensor or scalar
提示
The probability density function for the noncentral Chi-square distribution is
\[P(x;df,nonc) = \sum^{\infty}_{i=0} \frac{e^{-nonc/2}(nonc/2)^{i}}{i!} \P_{Y_{df+2i}}(x),\]where \(Y_{q}\) 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.
引用
- 1
Delhi, M.S. Holla, “On a noncentral chi-square distribution in the analysis of weapon systems effectiveness”, Metrika, Volume 15, Number 1 / December, 1970.
- 2
Wikipedia, “Noncentral chi-square distribution” http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution
实际案例
Draw values from the distribution and plot the histogram
>>> import matplotlib.pyplot as plt >>> import mars.tensor as mt >>> values = plt.hist(mt.random.noncentral_chisquare(3, 20, 100000).execute(), ... bins=200, normed=True) >>> plt.show()
Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare.
>>> plt.figure() >>> values = plt.hist(mt.random.noncentral_chisquare(3, .0000001, 100000).execute(), ... bins=mt.arange(0., 25, .1).execute(), normed=True) >>> values2 = plt.hist(mt.random.chisquare(3, 100000).execute(), ... bins=mt.arange(0., 25, .1).execute(), normed=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(mt.random.noncentral_chisquare(3, 20, 100000).execute(), ... bins=200, normed=True) >>> plt.show()