def reg_score_function(X, y, mean, scale, shape, skewness):
        """ GAS Cauchy Regression Update term using gradient only - native Python function

        Parameters
        ----------
        X : float
            datapoint for the right hand side variable
    
        y : float
            datapoint for the time series

        mean : float
            location parameter 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
        ----------
        - Score of the Cauchy family
        """
        return 2.0*((y-mean)*X)/(np.power(scale,2)+np.power((y-mean),2))
GAS Cauchy Regression Update term using gradient only - native Python function

        Parameters
        ----------
        X : float
            datapoint for the right hand side variable
    
        y : float
            datapoint for the time series

        mean : float
            location parameter 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
        ----------
        - Score of the Cauchy family