noncentral_f(self, dfnum, dfden, nonc, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.noncentral_f.
Some inconsistencies with the Dask version may exist.
Samples are drawn from an F distribution with specified parameters, :None:None:`dfnum` (degrees of freedom in numerator) and :None:None:`dfden` (degrees of freedom in denominator), where both parameters > 1. :None:None:`nonc` is the non-centrality parameter.
New code should use the noncentral_f
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
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.
Numerator degrees of freedom, must be > 0.
Earlier NumPy versions required dfnum > 1.
Denominator degrees of freedom, must be > 0.
Non-centrality parameter, the sum of the squares of the numerator means, must be >= 0.
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.
Drawn samples from the parameterized noncentral Fisher distribution.
Draw samples from the noncentral F distribution.
Generator.noncentral_f
which should be used for new code.
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.
This example is valid syntax, but we were not able to check execution>>> dfnum = 3 # between group deg of freedom # doctest: +SKIPSee :
... dfden = 20 # within groups degrees of freedom # doctest: +SKIP
... nonc = 3.0 # doctest: +SKIP
... nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000) # doctest: +SKIP
... NF = np.histogram(nc_vals, bins=50, density=True) # doctest: +SKIP
... c_vals = np.random.f(dfnum, dfden, 1000000) # doctest: +SKIP
... F = np.histogram(c_vals, bins=50, density=True) # doctest: +SKIP
... import matplotlib.pyplot as plt # doctest: +SKIP
... plt.plot(F[1][1:], F[0]) # doctest: +SKIP
... plt.plot(NF[1][1:], NF[0]) # doctest: +SKIP
... plt.show() # doctest: +SKIP
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