noncentral_f(dfnum, dfden, nonc, size=None, chunk_size=None, gpu=None, dtype=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.
dfnum (float or array_like of floats) – Numerator degrees of freedom, should be > 0.
dfden (float or array_like of floats) – Denominator degrees of freedom, should be > 0.
nonc (float or array_like of floats) – Non-centrality 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), then
m * n * ksamples are drawn. If size is
None(default), a single value is returned if
noncare all scalars. Otherwise,
np.broadcast(dfnum, dfden, nonc).sizesamples are drawn.
chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension
gpu (bool, optional) – Allocate the tensor on GPU if True, False as default
dtype (data-type, optional) – Data-type of the returned tensor.
out – Drawn samples from the parameterized noncentral Fisher distribution.
- Return type
Tensor or scalar
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.
Weisstein, Eric W. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html
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.
>>> import mars.tensor as mt >>> import matplotlib.pyplot as plt
>>> dfnum = 3 # between group deg of freedom >>> dfden = 20 # within groups degrees of freedom >>> nonc = 3.0 >>> nc_vals = mt.random.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals.execute(), bins=50, normed=True) # TODO(jisheng): implement mt.histogram >>> c_vals = mt.random.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals.execute(), bins=50, normed=True) >>> plt.plot(F[1:], F) >>> plt.plot(NF[1:], NF) >>> plt.show()