code: def logpdf_link(self, link_f, y, Y_metadata=None):
          
          # alpha = self.gp_link.transf(gp)*self.beta    sum(log(a) + (a-1).*log(y)- f - exp(-f).*y.^a)
          # return (1. - alpha)*np.log(obs) + self.beta*obs - alpha * np.log(self.beta) + np.log(special.gamma(alpha))
          assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
          c = np.zeros_like(y)
          if Y_metadata is not None and 'censored' in Y_metadata.keys():
              c = Y_metadata['censored']
  
          # uncensored = (1-c)* (np.log(self.r) + (self.r - 1) * np.log(y) - link_f - (np.exp(-link_f) * (y ** self.r)))
          # censored = (-c)*np.exp(-link_f)*(y**self.r)
          uncensored = (1-c)*( np.log(self.r)-np.log(link_f)+(self.r-1)*np.log(y) - y**self.r/link_f)
          censored = -c*y**self.r/link_f
  
          log_objective = uncensored + censored
          return log_objective
docs: 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