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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code: def _mean(self):
      if self.allow_nan_stats:
          return tf.fill(
              self.batch_shape_tensor(),
              dtype_util.as_numpy_dtype(self.dtype)(np.nan),
          )
      else:
          raise ValueError(
              "`mean` is undefined for Cauchy distribution."
          )
  
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 16 for calling the Cauchy obj's underlying member method code with example usage: obj._mean() and returns: tf