class_docstr: LambertWTail transformation for heavy-tail Lambert W x F random variables.
  
  A random variable Y has a Lambert W x F distribution if W_tau(Y) = X has
  distribution F, where tau = (shift, scale, tail) parameterizes the inverse
  transformation.
  
  This bijector defines the transformation underlying Lambert W x F
  distributions that transform an input random variable to an output
  random variable with heavier tails. It is defined as
  
    Y = (U * exp(0.5 * tail * U^2)) * scale + shift,  tail >= 0
  
  where U = (X - shift) / scale is a shifted/scaled input random variable, and
  tail >= 0 is the tail parameter.
  
  Attributes:
    shift: shift to center (uncenter) the input data.
    scale: scale to normalize (de-normalize) the input data.
    tailweight: Tail parameter `delta` of heavy-tail transformation; must be
      >= 0.
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code: def _parameter_properties(cls, dtype):
      return dict(
          shift=parameter_properties.ParameterProperties(),
          scale=parameter_properties.ParameterProperties(
              default_constraining_bijector_fn=(
                  lambda: tfb_softplus.Softplus(
                      low=dtype_util.eps(dtype)
                  )
              )
          ),
          tailweight=parameter_properties.ParameterProperties(
              default_constraining_bijector_fn=(
                  lambda: tfb_softplus.Softplus(
                      low=dtype_util.eps(dtype)
                  )
              )
          ),
      )
  
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import bijector
  from tensorflow_probability.python.bijectors import chain
  from tensorflow_probability.python.bijectors import invert
  from tensorflow_probability.python.bijectors import scale
  from tensorflow_probability.python.bijectors import shift
  from tensorflow_probability.python.bijectors import softplus
  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 tensor_util
  from tensorflow_probability.python.math import special
label_desc: Use image node_id 2 for calling the LambertWTail obj's underlying member method code with example usage: obj._parameter_properties(cls, dtype) and returns: dict