numpy.random.RandomState.noncentral_f¶
method

RandomState.
noncentral_f
(dfnum, dfden, nonc, size=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 noncentrality parameter.
Note
New code should use the
noncentral_f
method of adefault_rng()
instance instead; see randomquickstart. Parameters
 dfnumfloat or array_like of floats
Numerator degrees of freedom, must be > 0.
Changed in version 1.14.0: Earlier NumPy versions required dfnum > 1.
 dfdenfloat or array_like of floats
Denominator degrees of freedom, must be > 0.
 noncfloat or array_like of floats
Noncentrality parameter, the sum of the squares of the numerator means, must be >= 0.
 sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifdfnum
,dfden
, andnonc
are all scalars. Otherwise,np.broadcast(dfnum, dfden, nonc).size
samples are drawn.
 Returns
 outndarray or scalar
Drawn samples from the parameterized noncentral Fisher distribution.
See also
Generator.noncentral_f
which should be used for new code.
Notes
When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the noncentral 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 noncentral F statistic.
References
 1
Weisstein, Eric W. “Noncentral FDistribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralFDistribution.html
 2
Wikipedia, “Noncentral Fdistribution”, https://en.wikipedia.org/wiki/Noncentral_Fdistribution
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 = np.random.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals, bins=50, density=True) >>> c_vals = np.random.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()