ncinv(a, b, y, out=None)

    Inverse of the regularized incomplete beta function.

    Computes :math:`x` such that:

    .. math::

        y = I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
        \int_0^x t^{a-1}(1-t)^{b-1}dt,

    where :math:`I_x` is the normalized incomplete beta function `betainc`
    and :math:`\Gamma` is the `gamma` function [1]_.

    Parameters
    ----------
    a, b : array_like
        Positive, real-valued parameters
    y : array_like
        Real-valued input
    out : ndarray, optional
        Optional output array for function values

    Returns
    -------
    scalar or ndarray
        Value of the inverse of the regularized incomplete beta function

    See Also
    --------
    betainc : regularized incomplete beta function
    gamma : gamma function

    Notes
    -----
    This function wraps the ``ibeta_inv`` routine from the
    Boost Math C++ library [2]_.

    References
    ----------
    .. [1] NIST Digital Library of Mathematical Functions
           https://dlmf.nist.gov/8.17
    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

    Examples
    --------
    >>> import scipy.special as sc

    This function is the inverse of `betainc` for fixed
    values of :math:`a` and :math:`b`.

    >>> a, b = 1.2, 3.1
    >>> y = sc.betainc(a, b, 0.2)
    >>> sc.betaincinv(a, b, y)
    0.2
    >>>
    >>> a, b = 7.5, 0.4
    >>> x = sc.betaincinv(a, b, 0.5)
    >>> sc.betainc(a, b, x)
    0.5

    