Module « numpy.random »

Fonction f - module numpy.random

Signature de la fonction f

Description

f.__doc__

        f(dfnum, dfden, size=None)

        Draw samples from an 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 must be greater than
        zero.

        The random variate of the F distribution (also known as the
        Fisher distribution) is a continuous probability distribution
        that arises in ANOVA tests, and is the ratio of two chi-square
        variates.

        .. note::
            New code should use the ``f`` method of a ``default_rng()``
            instance instead; please see the :ref:`random-quick-start`.

        Parameters
        ----------
        dfnum : float or array_like of floats
            Degrees of freedom in numerator, must be > 0.
        dfden : float or array_like of float
            Degrees of freedom in denominator, must be > 0.
        size : int or tuple of ints, optional
            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn.  If size is ``None`` (default),
            a single value is returned if ``dfnum`` and ``dfden`` are both scalars.
            Otherwise, ``np.broadcast(dfnum, dfden).size`` samples are drawn.

        Returns
        -------
        out : ndarray or scalar
            Drawn samples from the parameterized Fisher distribution.

        See Also
        --------
        scipy.stats.f : probability density function, distribution or
            cumulative density function, etc.
        Generator.f: which should be used for new code.

        Notes
        -----
        The F statistic is used to compare in-group variances to between-group
        variances. Calculating the distribution depends on the sampling, and
        so it is a function of the respective degrees of freedom in the
        problem.  The variable `dfnum` is the number of samples minus one, the
        between-groups degrees of freedom, while `dfden` is the within-groups
        degrees of freedom, the sum of the number of samples in each group
        minus the number of groups.

        References
        ----------
        .. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
               Fifth Edition, 2002.
        .. [2] Wikipedia, "F-distribution",
               https://en.wikipedia.org/wiki/F-distribution

        Examples
        --------
        An example from Glantz[1], pp 47-40:

        Two groups, children of diabetics (25 people) and children from people
        without diabetes (25 controls). Fasting blood glucose was measured,
        case group had a mean value of 86.1, controls had a mean value of
        82.2. Standard deviations were 2.09 and 2.49 respectively. Are these
        data consistent with the null hypothesis that the parents diabetic
        status does not affect their children's blood glucose levels?
        Calculating the F statistic from the data gives a value of 36.01.

        Draw samples from the distribution:

        >>> dfnum = 1. # between group degrees of freedom
        >>> dfden = 48. # within groups degrees of freedom
        >>> s = np.random.f(dfnum, dfden, 1000)

        The lower bound for the top 1% of the samples is :

        >>> np.sort(s)[-10]
        7.61988120985 # random

        So there is about a 1% chance that the F statistic will exceed 7.62,
        the measured value is 36, so the null hypothesis is rejected at the 1%
        level.