code: def neg_loglikelihood(y, mean, scale, shape, skewness):
          
          return -np.sum(ss.cauchy.logpdf(y, loc=mean, scale=scale))
docs: 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