def pdf_link(self, link_f, y, Y_metadata=None):
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape<EOL>alpha = link_f*self.beta<EOL>objective = (y**(alpha - <NUM_LIT:1.>) * np.exp(-self.beta*y) * self.beta**alpha)/ special.gamma(alpha)<EOL>return np.exp(np.sum(np.log(objective)))<EOL>
Likelihood function given link(f)

.. math::
    p(y_{i}|\\lambda(f_{i})) = \\frac{\\beta^{\\alpha_{i}}}{\\Gamma(\\alpha_{i})}y_{i}^{\\alpha_{i}-1}e^{-\\beta y_{i}}\\\\
    \\alpha_{i} = \\beta y_{i}

:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
:param Y_metadata: Y_metadata which is not used in poisson distribution
:returns: likelihood evaluated for this point
:rtype: float