class_docstr: The Cauchy distribution with location `loc` and scale `scale`.
  
  #### Mathematical details
  
  The probability density function (pdf) is,
  
  ```none
  pdf(x; loc, scale) = 1 / (pi scale (1 + z**2))
  z = (x - loc) / scale
  ```
  where `loc` is the location, and `scale` is the scale.
  
  The Cauchy distribution is a member of the [location-scale family](
  https://en.wikipedia.org/wiki/Location-scale_family), i.e.
  `Y ~ Cauchy(loc, scale)` is equivalent to,
  
  ```none
  X ~ Cauchy(loc=0, scale=1)
  Y = loc + scale * X
  ```
  
  #### Examples
  
  Examples of initialization of one or a batch of distributions.
  
  ```python
  tfd = tfp.distributions
  
  # Define a single scalar Cauchy distribution.
  dist = tfd.Cauchy(loc=0., scale=3.)
  
  # Evaluate the cdf at 1, returning a scalar.
  dist.cdf(1.)
  
  # Define a batch of two scalar valued Cauchy distributions.
  dist = tfd.Cauchy(loc=[1, 2.], scale=[11, 22.])
  
  # Evaluate the pdf of the first distribution on 0, and the second on 1.5,
  # returning a length two tensor.
  dist.prob([0, 1.5])
  
  # Get 3 samples, returning a 3 x 2 tensor.
  dist.sample([3])
  
  # Arguments are broadcast when possible.
  # Define a batch of two scalar valued Cauchy distributions.
  # Both have median 1, but different scales.
  dist = tfd.Cauchy(loc=1., scale=[11, 22.])
  
  # Evaluate the pdf of both distributions on the same point, 3.0,
  # returning a length 2 tensor.
  dist.prob(3.)
  ```
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docstr: Construct Cauchy distributions.
  
  The parameters `loc` and `scale` must be shaped in a way that supports
  broadcasting (e.g. `loc + scale` is a valid operation).
  
  Args:
    loc: Floating point tensor; the modes of the distribution(s).
    scale: Floating point tensor; the half-widths of the distribution(s) at
      their half-maximums. Must contain only positive values.
    validate_args: Python `bool`, default `False`. When `True` distribution
      parameters are checked for validity despite possibly degrading runtime
      performance. When `False` invalid inputs may silently render incorrect
      outputs.
    allow_nan_stats: Python `bool`, default `True`. When `True`,
      statistics (e.g., mean, mode, variance) use the value '`NaN`' to
      indicate the result is undefined. When `False`, an exception is raised
      if one or more of the statistic's batch members are undefined.
    name: Python `str` name prefixed to Ops created by this class.
  
  Raises:
    TypeError: if `loc` and `scale` have different `dtype`.
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code: def __init__(
      self,
      loc,
      scale,
      validate_args=False,
      allow_nan_stats=True,
      name="Cauchy",
  ):
      """Construct Cauchy distributions.
  
      The parameters `loc` and `scale` must be shaped in a way that supports
      broadcasting (e.g. `loc + scale` is a valid operation).
  
      Args:
        loc: Floating point tensor; the modes of the distribution(s).
        scale: Floating point tensor; the half-widths of the distribution(s) at
          their half-maximums. Must contain only positive values.
        validate_args: Python `bool`, default `False`. When `True` distribution
          parameters are checked for validity despite possibly degrading runtime
          performance. When `False` invalid inputs may silently render incorrect
          outputs.
        allow_nan_stats: Python `bool`, default `True`. When `True`,
          statistics (e.g., mean, mode, variance) use the value '`NaN`' to
          indicate the result is undefined. When `False`, an exception is raised
          if one or more of the statistic's batch members are undefined.
        name: Python `str` name prefixed to Ops created by this class.
  
      Raises:
        TypeError: if `loc` and `scale` have different `dtype`.
      """
      parameters = dict(locals())
      with tf.name_scope(name) as name:
          dtype = dtype_util.common_dtype([loc, scale], tf.float32)
          self._loc = tensor_util.convert_nonref_to_tensor(
              loc, name="loc", dtype=dtype
          )
          self._scale = tensor_util.convert_nonref_to_tensor(
              scale, name="scale", dtype=dtype
          )
          dtype_util.assert_same_float_dtype([self._loc, self._scale])
          super(Cauchy, self).__init__(
              dtype=self._scale.dtype,
              reparameterization_type=reparameterization.FULLY_REPARAMETERIZED,
              validate_args=validate_args,
              allow_nan_stats=allow_nan_stats,
              parameters=parameters,
              name=name,
          )
  
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import identity
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.distributions import kullback_leibler
  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 1 to create a new Cauchy object from inherited base classes: distribution with example: obj = Cauchy(loc, scale, validate_args, allow_nan_stats, name)