GAS Poisson Update term potentially using second-order information - native Python function

        Parameters
        ----------
        y : float
            datapoint for the time series

        mean : float
            location parameter for the Poisson distribution

        scale : float
            scale parameter for the Poisson distribution

        shape : float
            tail thickness parameter for the Poisson distribution

        skewness : float
            skewness parameter for the Poisson distribution

        Returns
        ----------
        - Adjusted score of the Poisson family

def second_order_score(y, mean, scale, shape, skewness):
        """ GAS Poisson Update term potentially using second-order information - native Python function

        Parameters
        ----------
        y : float
            datapoint for the time series

        mean : float
            location parameter for the Poisson distribution

        scale : float
            scale parameter for the Poisson distribution

        shape : float
            tail thickness parameter for the Poisson distribution

        skewness : float
            skewness parameter for the Poisson distribution

        Returns
        ----------
        - Adjusted score of the Poisson family
        """
        return (y-mean)/float(mean)