noncentral_f

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noncentral_f#

class brainstate.random.noncentral_f(dfnum, dfden, nonc, size=None, key=None, dtype=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.

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 | Sequence[int] | integer | Sequence[integer] | None) – 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.

  • key (int | Array | ndarray | None) – The key for the random number generator. If not given, the default random number generator is used.

Returns:

out – Drawn samples from the parameterized noncentral Fisher distribution.

Return type:

ndarray or scalar

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

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.

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