class_docstr: Cauchy Distribution
  ----
  This class contains methods relating to the Cauchy distribution for time series.
docstr: Markov blanket for each likelihood term - used for state space models
  
  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
  ----------
  - Markov blanket of the Cauchy family
docstr_tok: ["Markov","blanket","for","each","likelihood","term","-","used","for","state","space","models","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","--","--","--","--","--","-","Markov","blanket","of","the","Cauchy","family"]
code: def markov_blanket(y, mean, scale, shape, skewness):
      """Markov blanket for each likelihood term - used for state space models
  
      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
      ----------
      - Markov blanket of the Cauchy family
      """
      return ss.cauchy.logpdf(y, loc=mean, scale=scale)
  
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 8 for calling the Cauchy obj's underlying member method code with example usage: obj.markov_blanket(y, mean, scale, shape, skewness) and returns: ss