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 non-centrality parameter.
Parameters: |
dfnum : int or array_like of ints Parameter, should be > 1. dfden : int or array_like of ints Parameter, should be > 1. nonc : float or array_like of floats Parameter, should be >= 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., |
---|---|
Returns: |
out : ndarray or scalar Drawn samples from the parameterized noncentral Fisher distribution. |
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.
[R181] | Weisstein, Eric W. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html |
[R182] | Wikipedia, “Noncentral F-distribution”, http://en.wikipedia.org/wiki/Noncentral_F-distribution |
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, normed=True) >>> c_vals = np.random.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals, bins=50, normed=True) >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> plt.show()
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https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.random.RandomState.noncentral_f.html