class_docstr: Cauchy Distribution
  ----
  This class contains methods relating to the Cauchy distribution for time series.
docstr: Parameters
  ----------
  loc : float
      Location parameter for the Cauchy distribution
  
  sigma : float
      Dispersion parameter for the Cauchy distribution
  
  transform : str
      Whether to apply a transformation - e.g. 'exp' or 'logit'
docstr_tok: ["Parameters","--","--","--","--","--","loc",":","float","Location","parameter","for","the","Cauchy","distribution","sigma",":","float","Dispersion","parameter","for","the","Cauchy","distribution","transform",":","str","Whether","to","apply","a","transformation","-","e.g",".","'exp","'","or","'logit","'"]
code: def __init__(self, loc=0.0, scale=1.0, transform=None, **kwargs):
      """
      Parameters
      ----------
      loc : float
          Location parameter for the Cauchy distribution
  
      sigma : float
          Dispersion parameter for the Cauchy distribution
  
      transform : str
          Whether to apply a transformation - e.g. 'exp' or 'logit'
      """
      super(Cauchy, self).__init__(transform)
      self.loc0 = loc
      self.scale0 = scale
      self.covariance_prior = False
  
      self.gradient_only = kwargs.get(
          "gradient_only", False
      )  # used for GAS t models
      if self.gradient_only is True:
          self.score_function = self.first_order_score
      else:
          self.score_function = self.second_order_score
  
imports: import numpy
  import scipy.stats
  import scipy.special
  from .family import Family
  from .flat import Flat
  from .normal import Normal
  from .gas_recursions import gas_recursion_cauchy_orderone, gas_recursion_cauchy_ordertwo
  from .gas_recursions import gasx_recursion_cauchy_orderone, gasx_recursion_cauchy_ordertwo
  from .gas_recursions import gas_llev_recursion_cauchy_orderone, gas_llev_recursion_cauchy_ordertwo
  from .gas_recursions import gas_llt_recursion_cauchy_orderone, gas_llt_recursion_cauchy_ordertwo
  from .gas_recursions import gas_reg_recursion_cauchy_orderone, gas_reg_recursion_cauchy_ordertwo
label_desc: Use image node_id 1 to create a new Cauchy object from inherited base classes: Family with example: obj = Cauchy(loc, scale, transform)