code: def second_order_score(y, mean, scale, shape, skewness):
          
          return (y-mean)/float(mean)
docs: 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