`numpy.random._generator:Generator.noncentral_f`

Signature

def noncentral_f ( dfnum , dfden , nonc , size = None )

Summary

Draw samples from the noncentral F distribution.

Extended Summary

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 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.

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.

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.

rng = np.random.default_rng()
dfnum = 3 # between group deg of freedom
dfden = 20 # within groups degrees of freedom
nonc = 3.0
nc_vals = rng.noncentral_f(dfnum, dfden, nonc, 1000000)
NF = np.histogram(nc_vals, bins=50, density=True)
c_vals = rng.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()

✓

Aliases

numpy.random.Generator.noncentral_f