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# 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 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 > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., `(m, n, k)`, then `m * 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

  [R245] | Delhi, M.S. Holla, “On a noncentral chi-square distribution in the analysis of weapon systems effectiveness”, Metrika, Volume 15, Number 1 / December, 1970.

  [R246] | Wikipedia, “Noncentral chi-square distribution” http://en.wikipedia.org/wiki/Noncentral_chi-square_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, 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)