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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) anddfden(degrees of freedom in denominator), where both parameters > 1.noncis the non-centrality parameter.Parameters: dfnum : int
Parameter, should be > 1.
dfden : int
Parameter, should be > 1.
nonc : float
Parameter, should be >= 0.
size : int or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k), thenm * n * ksamples are drawn. Default is None, in which case a single value is returned.Returns: samples : scalar or ndarray
Drawn samples.
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.
References
[R247] Weisstein, Eric W. ?Noncentral F-Distribution.? From MathWorld?A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html [R248] Wikipedia, ?Noncentral F distribution?, http://en.wikipedia.org/wiki/Noncentral_F-distribution 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.
12345678910>>> 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()
numpy.random.noncentral_f()
2025-01-10 15:47:30
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