flopscope.

flopscope.numpy.random.RandomState.noncentral_f

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

Draw samples from the noncentral F distribution.

Adapted from NumPy docs np.random.RandomState.noncentral_f

Arearandom
Typecounted
NumPy Refnp.random.RandomState.noncentral_f
Cost
numel(output)\text{numel}(\text{output})
Flopscope Context

Legacy noncentral F; cost = numel(output).

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 random-quick-start.

Parameters

dfnum:float or array_like of floats

Numerator degrees of freedom, must be > 0.

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, flops.broadcast(dfnum, dfden, nonc).size samples are drawn.

Returns

out:ndarray or scalar

Drawn samples from the parameterized noncentral Fisher distribution.

See also

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

footnote
1

Weisstein, Eric W. "Noncentral F-Distribution."
From MathWorld--A Wolfram Web Resource.
https://mathworld.wolfram.com/NoncentralF-Distribution.html
footnote
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 = flops.random.noncentral_f(dfnum, dfden, nonc, 1000000)
>>> NF = flops.histogram(nc_vals, bins=50, density=True)
>>> c_vals = flops.random.f(dfnum, dfden, 1000000)
>>> F = flops.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()