numpy.random.noncentral_f¶

numpy.random.
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.
Parameters:  dfnum : float or array_like of floats
Numerator degrees of freedom, should be > 0.
Changed in version 1.14.0: Earlier NumPy versions required dfnum > 1.
 dfden : float or array_like of floats
Denominator degrees of freedom, should be > 0.
 nonc : float or array_like of floats
Noncentrality parameter, the sum of the squares of the numerator means, should be >= 0.
 size : int 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:  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 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”, http://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) >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> plt.show()