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.

tfb_lambert_w_tail(
  shift = NULL,
  scale = NULL,
  tailweight = NULL,
  validate_args = FALSE,
  name = "lambertw_tail"
)

Arguments

shift

Floating point tensor; the shift for centering (uncentering) the input (output) random variable(s).

scale

Floating point tensor; the scaling (unscaling) of the input (output) random variable(s). Must contain only positive values.

tailweight

Floating point tensor; the tail behaviors of the output random variable(s). Must contain only non-negative values.

validate_args

Logical, default FALSE. Whether to validate input with asserts. If validate_args is FALSE, and the inputs are invalid, correct behavior is not guaranteed.

name

name prefixed to Ops created by this class.

Value

a bijector instance.

Details

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.

See also