def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
        """
        Gradient of the pdf at y, given inverse link of f w.r.t inverse link of f.

        .. math::
            \\frac{d^{2}\\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)^{2}} = \\frac{y_{i}}{\\lambda(f)} - \\frac{(N-y_{i})}{(1-\\lambda(f))}

        :param inv_link_f: latent variables inverse link of f.
        :type inv_link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata must contain 'trials'
        :returns: gradient of log likelihood evaluated at points inverse link of f.
        :rtype: Nx1 array
        """
        N = Y_metadata['trials']
        np.testing.assert_array_equal(N.shape, y.shape)

        Ny = N-y
        t1 = np.zeros(y.shape)
        t2 = np.zeros(y.shape)
        t1[y>0] = y[y>0]/inv_link_f[y>0]
        t2[Ny>0] = (Ny[Ny>0])/(1.-inv_link_f[Ny>0])        

        return t1 - t2