def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None):
        """
        Third order derivative log-likelihood function at y given link(f) w.r.t link(f)

        .. math::
            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \lambda(f_{i}))^3 - 3(y_{i} - \lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \lambda(f_{i})) + \\sigma^{2} v)^3}

        :param inv_link_f: latent variables link(f)
        :type inv_link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata which is not used in student t distribution
        :returns: third derivative of likelihood evaluated at points f
        :rtype: Nx1 array
        """
        e = y - inv_link_f
        d3lik_dlink3 = ( -(2*(self.v + 1)*(-e)*(e**2 - 3*self.v*self.sigma2)) /
                       ((e**2 + self.sigma2*self.v)**3)
                    )
        return d3lik_dlink3
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)

        .. math::
            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \lambda(f_{i}))^3 - 3(y_{i} - \lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \lambda(f_{i})) + \\sigma^{2} v)^3}

        :param inv_link_f: latent variables link(f)
        :type inv_link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata which is not used in student t distribution
        :returns: third derivative of likelihood evaluated at points f
        :rtype: Nx1 array