class_docstr: Cauchy Distribution
  ----
  This class contains methods relating to the Cauchy distribution for time series.
docstr: Returns the attributes of this family if using in a probabilistic model
  
  Notes
  ----------
  - scale notes whether family has a variance parameter (sigma)
  - shape notes whether family has a tail thickness parameter (nu)
  - skewness notes whether family has a skewness parameter (gamma)
  - mean_transform is a function which transforms the location parameter
  - cythonized notes whether the family has cythonized routines
  
  Returns
  ----------
  - model name, link function, scale, shape, skewness, mean_transform, cythonized
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code: def setup():
      """Returns the attributes of this family if using in a probabilistic model
  
      Notes
      ----------
      - scale notes whether family has a variance parameter (sigma)
      - shape notes whether family has a tail thickness parameter (nu)
      - skewness notes whether family has a skewness parameter (gamma)
      - mean_transform is a function which transforms the location parameter
      - cythonized notes whether the family has cythonized routines
  
      Returns
      ----------
      - model name, link function, scale, shape, skewness, mean_transform, cythonized
      """
      name = "Cauchy"
      link = np.array
      scale = True
      shape = False
      skewness = False
      mean_transform = np.array
      cythonized = True  # used for GAS models
      return (
          name,
          link,
          scale,
          shape,
          skewness,
          mean_transform,
          cythonized,
      )
  
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 9 for calling the Cauchy obj's underlying member method code with example usage: obj.setup() and returns: name,  link,  scale,  shape,  skewness,  mean_transform,  cythonized