`numpy.random._generator:Generator.f`

Signature

def f ( dfnum , dfden , size = None )

Summary

Draw samples from an 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 must be greater than zero.

The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates.

Parameters

dfnum : float or array_like of floats: Degrees of freedom in numerator, must be > 0.
dfden : float or array_like of float: Degrees of freedom in denominator, 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 and dfden are both scalars. Otherwise, np.broadcast(dfnum, dfden).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized Fisher distribution.

Notes

The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable dfnum is the number of samples minus one, the between-groups degrees of freedom, while dfden is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups.

Examples

An example from Glantz [1]_, pp 47-40: Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children's blood glucose levels? Calculating the F statistic from the data gives a value of 36.01. Draw samples from the distribution:

dfnum = 1. # between group degrees of freedom
dfden = 48. # within groups degrees of freedom
rng = np.random.default_rng()
s = rng.f(dfnum, dfden, 1000)

✓

The lower bound for the top 1% of the samples is :

np.sort(s)[-10]

✗

So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level. The corresponding probability density function for ``n = 20`` and ``m = 20`` is:

import matplotlib.pyplot as plt
from scipy import stats
dfnum, dfden, size = 20, 20, 10000
s = rng.f(dfnum=dfnum, dfden=dfden, size=size)
bins, density, _ = plt.hist(s, 30, density=True)
x = np.linspace(0, 5, 1000)

✓

plt.plot(x, stats.f.pdf(x, dfnum, dfden))
plt.xlim([0, 5])

✗

plt.show()

✓

Aliases

numpy.random.Generator.f