code: def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
          
          # grad =  (1. - self.beta) / (y - link_f)
          c = np.zeros_like(y)
          if Y_metadata is not None and 'censored' in Y_metadata.keys():
              c = Y_metadata['censored']
  
          # uncensored = (1-c)* ( -1 + np.exp(-link_f)*(y ** self.r))
          # censored = c*np.exp(-link_f)*(y**self.r)
          uncensored = (1-c)*(-1/link_f + y**self.r/link_f**2)
          censored = c*y**self.r/link_f**2
          grad = uncensored + censored
          return grad
docs: Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
  
          .. math::
              \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\beta (\\log \\beta y_{i}) - \\Psi(\\alpha_{i})\\beta\\\\
              \\alpha_{i} = \\beta y_{i}
  
          :param link_f: latent variables (f)
          :type link_f: Nx1 array
          :param y: data
          :type y: Nx1 array
          :param Y_metadata: Y_metadata which is not used in gamma distribution
          :returns: gradient of likelihood evaluated at points
          :rtype: Nx1 array