def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None):
e = y - inv_link_f<EOL>d3lik_dlink3 = ( -(<NUM_LIT:2>*(self.v + <NUM_LIT:1>)*(-e)*(e**<NUM_LIT:2> - <NUM_LIT:3>*self.v*self.sigma2)) /<EOL>((e**<NUM_LIT:2> + self.sigma2*self.v)**<NUM_LIT:3>)<EOL>)<EOL>return d3lik_dlink3<EOL>
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