class_docstr: Implements a general heavy-tail Lambert W x F distribution.
  
  Lambert W x F random variables are a transformed version of a random variables
  with distribution F that have heavier tails. In particular, they are defined
  as a (non-linear) transformation of random variables X with distribution F.
  It therefore is straightforward to implement Lambert W x F distributions as a
  particular TransformedDistribution, where the input can be specified by user
  as any TensorFlow Distribution class.
  
  ### Mathematical Details
  
  Let X be a random variable following distribution F with mean mu
  and standard deviation sigma, define as U = (X-mu)/sigma its zero-mean,
  unit-variance version. Then
  
  Y = (U * exp (delta/2 * U^2)) * sigma + mu
  
  is a location-scale heavy-tailed Lambert W x F with parameters mu,
  sigma and delta, where delta can take any non-negative real value. In
  particular, for delta = 0, the Lambert W x F distribution reduces to the
  F distribution. That is F distributions are a subset of Lambert W x
  F distributions.
  
  See `tfp.bijectors.LambertWTail` for details on the transformation.
  
  ### References:
  [1]: Goerg, G.M., 2011. Lambert W random variables - a new family of
  generalized skewed distributions with applications to risk estimation.
  The Annals of Applied Statistics, 5(3), pp.2197-2230.
  [2]: Goerg, G.M., 2015. The Lambert way to Gaussianize heavy-tailed data with
  the inverse of Tukey's h transformation as a special case. The Scientific
  World Journal.
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docstr: Distribution parameter for the tail parameter delta.
docstr_tok: ["Distribution","parameter","for","the","tail","parameter","delta","."]
code: def tailweight(self):
      """Distribution parameter for the tail parameter delta."""
      return self._tailweight
  
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import identity
  from tensorflow_probability.python.bijectors import lambertw_transform
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import normal
  from tensorflow_probability.python.distributions import transformed_distribution
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import distribution_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import tensor_util
label_desc: Use image node_id 6 for calling the LambertWDistribution obj's underlying member method code with example usage: obj.tailweight() and returns: self