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# scipy.special.ncfdtr

`scipy.special.``ncfdtr`(dfn, dfd, nc, f) = <ufunc 'ncfdtr'>

  Cumulative distribution function of the non-central F distribution.

  Parameters: | dfn : array_like Degrees of freedom of the numerator sum of squares. Range (0, inf). dfd : array_like Degrees of freedom of the denominator sum of squares. Range (0, inf). nc : array_like Noncentrality parameter. Should be in range (0, 1e4). f : array_like Quantiles, i.e. the upper limit of integration.
  Returns: | cdf : float or ndarray The calculated CDF. If all inputs are scalar, the return will be a float. Otherwise it will be an array.

  See also

  `ncdfdtri`
    Inverse CDF (iCDF) of the non-central F distribution.
  `ncdfdtridfd`
    Calculate dfd, given CDF and iCDF values.
  `ncdfdtridfn`
    Calculate dfn, given CDF and iCDF values.
  `ncdfdtrinc`
    Calculate noncentrality parameter, given CDF, iCDF, dfn, dfd.

  Examples

      >>> from scipy import special
      >>> from scipy import stats
      >>> import matplotlib.pyplot as plt

  Plot the CDF of the non-central F distribution, for nc=0. Compare with the F-distribution from scipy.stats:

      >>> x = np.linspace(-1, 8, num=500)
      >>> dfn = 3
      >>> dfd = 2
      >>> ncf_stats = stats.f.cdf(x, dfn, dfd)
      >>> ncf_special = special.ncfdtr(dfn, dfd, 0, x)

      >>> fig = plt.figure()
      >>> ax = fig.add_subplot(111)
      >>> ax.plot(x, ncf_stats, 'b-', lw=3)
      >>> ax.plot(x, ncf_special, 'r-')
      >>> plt.show()

  (Source code)