def logpdf_link(self, link_f, y, Y_metadata=None):
        """
        Log Likelihood Function given link(f)

        .. math::
            \\ln p(y_{i}|\lambda(f_{i})) = \\ln \\lambda(f_{i}) - y_{i}\\lambda(f_{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 exponential distribution
        :returns: likelihood evaluated for this point
        :rtype: float

        """
        log_objective = np.log(link_f) - y*link_f
        return log_objective