def logpdf_link(self, link_f, y, Y_metadata=None):
<EOL>alpha = link_f*self.beta<EOL>log_objective = alpha*np.log(self.beta) - np.log(special.gamma(alpha)) + (alpha - <NUM_LIT:1>)*np.log(y) - self.beta*y<EOL>return log_objective<EOL>
Log Likelihood Function given link(f)

.. math::
    \\ln p(y_{i}|\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\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