class_docstr: Heavy tail transformation for Lambert W x F distributions.
  
  This bijector defines the transformation z = u * exp(0.5 * delta * u**2)
  and its inverse, where it is assumed that `u` is already an appropriately
  shifted & scaled input. It is the basis of the location-scale heavy-tail
  Lambert W x F distributions / transformations.
  The effect of this transformation is that it adds heavy tails to input.
  
  Attributes:
    tailweight: Tail parameter `delta` of the transformation(s).
class_docstr_tok: ["Heavy","tail","transformation","for","Lambert","W","x","F","distributions",".","This","bijector","defines","the","transformation","z","=","u","*","exp","(","0.5","*","delta","*","u","*","*","2",")","and","its","inverse",",","where","it","is","assumed","that","`","u","`","is","already","an","appropriately","shifted","&","scaled","input",".","It","is","the","basis","of","the","location-scale","heavy-tail","Lambert","W","x","F","distributions","\/","transformations",".","The","effect","of","this","transformation","is","that","it","adds","heavy","tails","to","input",".","Attributes",":","tailweight",":","Tail","parameter","`","delta","`","of","the","transformation","(","s",")","."]
code: def _parameter_properties(cls, dtype):
      return dict(
          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 6 for calling the _HeavyTailOnly obj's underlying member method code with example usage: obj._parameter_properties(cls, dtype) and returns: dict