cdfFc
==============================================

Purpose
----------------
Computes the complement of the cumulative distribution function of the F distribution.

Format
----------------
.. function:: p = cdfFc(x, df_n, df_d)

    :param x: Values at which to evaluate the complement of the F distribution cdf. :math:`x > 0`.
    :type x: NxK matrix

    :param df_n: ExE conformable with *x*. Degrees of freedom of numerator, :math:`df_n > 0`.
    :type df_n: LxM matrix

    :param df_d: ExE conformable with *x* and *df_n*. Degrees of freedom of denominator, :math:`df_d > 0`.
    :type df_d: PxQ matrix

    :return p: Each element in *p* is the complement of the F distribution cdf value evaluated at the corresponding element in *x*.

    :rtype p: matrix, max(N,L,P) by max(K,M,Q)

Examples
----------------
:func:`cdffc` can be used to calculate a p-value from an F-statistic.

::

    /*
    ** Computing the parameters
    */
    // Number of observations
    n_obs = 100;

    // Number of variables
    n_vars = 5;

    df_n = n_vars;
    df_d = n_obs - n_vars - 1;

    // Value to calculate p_value at
    f_stat = 2.4;

    // Call cdfFc
    p_value = cdfFc(f_stat, df_n, df_d);
    print p_value;

will return:

::

    0.042803132

Remarks
------------

This procedure finds the complement of the F distribution cdf which equals

.. math:: 1 - G(x, df_n, df_d)

where *G* is the *F* cdf with *df_n* and *df_d* degrees of freedom. Thus, to get the *F* cdf, use:

::

    1 - cdfFc(x, df_n, df_d);

The complement of the cdf is computed because this is what is most
commonly needed in statistical applications, and because it can be
computed with fewer problems of roundoff error.

A -1 is returned for those elements with invalid inputs.

.. seealso:: Functions :func:`cdfBeta`, :func:`cdfChic`, :func:`cdfN`, :func:`cdfNc`, :func:`cdfTc`, :func:`gamma`