def neg_loglikelihood(y, mean, scale, shape, skewness):
        """ Negative loglikelihood function for this distribution

        Parameters
        ----------
        y : np.ndarray
            univariate time series

        mean : np.ndarray
            array of location parameters for the Cauchy distribution

        scale : float
            scale parameter for the Cauchy distribution

        shape : float
            tail thickness parameter for the Cauchy distribution

        skewness : float
            skewness parameter for the Cauchy distribution

        Returns
        ----------
        - Negative loglikelihood of the Cauchy family
        """
        return -np.sum(ss.cauchy.logpdf(y, loc=mean, scale=scale))