class_docstr: Half-Cauchy distribution.
  
  The half-Cauchy distribution is parameterized by a `loc` and a
  `scale` parameter. It represents the right half of the two symmetric halves in
  a [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution).
  
  #### Mathematical Details
  The probability density function (pdf) for the half-Cauchy distribution
  is given by
  
  ```none
  pdf(x; loc, scale) = 2 / (pi scale (1 + z**2))
  z = (x - loc) / scale
  ```
  
  where `loc` is a scalar in `R` and `scale` is a positive scalar in `R`.
  
  The support of the distribution is given by the interval `[loc, infinity)`.
class_docstr_tok: ["Half-Cauchy","distribution",".","The","half-Cauchy","distribution","is","parameterized","by","a","`","loc","`","and","a","`","scale","`","parameter",".","It","represents","the","right","half","of","the","two","symmetric","halves","in","a","[","Cauchy","distribution","]","(","https",":","\/\/en.wikipedia.org\/wiki\/Cauchy_distribution",")",".","#","#","#","#","Mathematical","Details","The","probability","density","function","(","pdf",")","for","the","half-Cauchy","distribution","is","given","by","``","`","none","pdf","(","x",";","loc",",","scale",")","=","2","\/","(","pi","scale","(","1","+","z","*","*","2",")",")","z","=","(","x","-","loc",")","\/","scale","``","`","where","`","loc","`","is","a","scalar","in","`","R","`","and","`","scale","`","is","a","positive","scalar","in","`","R","`",".","The","support","of","the","distribution","is","given","by","the","interval","`","[","loc",",","infinity",")","`","."]
code: def _parameter_properties(cls, dtype, num_classes=None):
      # pylint: disable=g-long-lambda
      return dict(
          loc=parameter_properties.ParameterProperties(),
          scale=parameter_properties.ParameterProperties(
              default_constraining_bijector_fn=(
                  lambda: softplus_bijector.Softplus(
                      low=dtype_util.eps(dtype)
                  )
              )
          ),
      )
  
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import chain
  from tensorflow_probability.python.bijectors import exp
  from tensorflow_probability.python.bijectors import shift
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import reparameterization
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import tensor_util
label_desc: Use image node_id 2 for calling the HalfCauchy obj's underlying member method code with example usage: obj._parameter_properties(cls, dtype, num_classes) and returns: dict