# numpy.random.noncentral_f

random.noncentral_f(dfnum, dfden, nonc, size=None)

  Draw samples from the noncentral F distribution.

  Samples are drawn from an F distribution with specified parameters, dfnum (degrees of freedom in numerator) and dfden (degrees of freedom in denominator), where both parameters > 1. nonc is the non-centrality parameter.

  Note

  New code should use the `noncentral_f` method of a `Generator` instance instead; please see the Quick Start.

  Parameters:
    dfnum float or array_like of floats

      Numerator degrees of freedom, must be > 0.

      Changed in version 1.14.0: Earlier NumPy versions required dfnum > 1.

    dfden float or array_like of floats

      Denominator degrees of freedom, must be > 0.

    nonc float or array_like of floats

      Non-centrality parameter, the sum of the squares of the numerator means, must 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. If size is `None` (default), a single value is returned if `dfnum`, `dfden`, and `nonc` are all scalars. Otherwise, `np.broadcast(dfnum, dfden, nonc).size` samples are drawn.

  Returns:
    out ndarray or scalar

      Drawn samples from the parameterized noncentral Fisher distribution.

  See also

  `random.Generator.noncentral_f`

    which should be used for new code.

  Notes

  When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic.

  References

  [1]

  Weisstein, Eric W. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html

  [2]

  Wikipedia, “Noncentral F-distribution”, https://en.wikipedia.org/wiki/Noncentral_F-distribution

  Examples

  In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We’ll plot the two probability distributions for comparison.

      >>> dfnum = 3 # between group deg of freedom
      >>> dfden = 20 # within groups degrees of freedom
      >>> nonc = 3.0
      >>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000)
      >>> NF = np.histogram(nc_vals, bins=50, density=True)
      >>> c_vals = np.random.f(dfnum, dfden, 1000000)
      >>> F = np.histogram(c_vals, bins=50, density=True)
      >>> import matplotlib.pyplot as plt
      >>> plt.plot(F[1][1:], F[0])
      >>> plt.plot(NF[1][1:], NF[0])
      >>> plt.show()