r ndarray
        The quantile corresponding to `p`.

    See Also
    --------
    fdtr : F distribution cumulative distribution function
    fdtrc : F distribution survival function
    scipy.stats.f : F distribution

    Notes
    -----
    The computation is carried out using the relation to the inverse
    regularized beta function, :math:`I^{-1}_x(a, b)`.  Let
    :math:`z = I^{-1}_p(d_d/2, d_n/2).`  Then,

    .. math::
        x = \frac{d_d (1 - z)}{d_n z}.

    If `p` is such that :math:`x < 0.5`, the following relation is used
    instead for improved stability: let
    :math:`z' = I^{-1}_{1 - p}(d_n/2, d_d/2).` Then,

    .. math::
        x = \frac{d_d z'}{d_n (1 - z')}.

    Wrapper for the Cephes [1]_ routine `fdtri`.

    The F distribution is also available as `scipy.stats.f`. Calling
    `fdtri` directly can improve performance compared to the ``ppf``
    method of `scipy.stats.f` (see last example below).

    References
    ----------
    .. [1] Cephes Mathematical Functions Library,
           http://www.netlib.org/cephes/

    Examples
    --------
    `fdtri` represents the inverse of the F distribution CDF which is
    available as `fdtr`. Here, we calculate the CDF for ``df1=1``, ``df2=2``
    at ``x=3``. `fdtri` then returns ``3`` given the same values for `df1`,
    `df2` and the computed CDF value.

    >>> import numpy as np
    >>> from scipy.special import fdtri, fdtr
    >>> df1, df2 = 1, 2
    >>> x = 3
    >>> cdf_value =  fdtr(df1, df2, x)
    >>> fdtri(df1, df2, cdf_value)
    3.000000000000006

    Calculate the function at several points by providing a NumPy array for
    `x`.

    >>> x = np.array([0.1, 0.4, 0.7])
    >>> fdtri(1, 2, x)
    array([0.02020202, 0.38095238, 1.92156863])

    Plot the function for several parameter sets.

    >>> import matplotlib.pyplot as plt
    >>> dfn_parameters = [50, 10, 1, 50]
    >>> dfd_parameters = [0.5, 1, 1, 5]
    >>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
    >>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
    ...                            linestyles))
    >>> x = np.linspace(0, 1, 1000)
    >>> fig, ax = plt.subplots()
    >>> for parameter_set in parameters_list:
    ...     dfn, dfd, style = parameter_set
    ...     fdtri_vals = fdtri(dfn, dfd, x)
    ...     ax.plot(x, fdtri_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
    ...             ls=style)
    >>> ax.legend()
    >>> ax.set_xlabel("$x$")
    >>> title = "F distribution inverse cumulative distribution function"
    >>> ax.set_title(title)
    >>> ax.set_ylim(0, 30)
    >>> plt.show()

    The F distribution is also available as `scipy.stats.f`. Using `fdtri`
    directly can be much faster than calling the ``ppf`` method of
    `scipy.stats.f`, especially for small arrays or individual values.
    To get the same results one must use the following parametrization:
    ``stats.f(dfn, dfd).ppf(x)=fdtri(dfn, dfd, x)``.

    >>> from scipy.stats import f
    >>> dfn, dfd = 1, 2
    >>> x = 0.7
    >>> fdtri_res = fdtri(dfn, dfd, x)  # this will often be faster than below
    >>> f_dist_res = f(dfn, dfd).ppf(x)
    >>> f_dist_res == fdtri_res  # test that results are equal
    True
    Úfdtridfdaz