numpy.random.noncentral_f — NumPy v1.11 Manual (original) (raw)
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 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 * k samples are drawn. Default is None, in which case a single value is returned. |
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| 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 |
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| [R248] | Wikipedia, “Noncentral F distribution”,http://en.wikipedia.org/wiki/Noncentral_F-distribution |
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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, 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()