LambertWTail transformation for heavy-tail Lambert W x F random variables.

Source: R/bijectors.R

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

For usage examples see tfb_forward(), tfb_inverse(), tfb_inverse_log_det_jacobian().

Other bijectors: tfb_absolute_value(), tfb_affine_linear_operator(), tfb_affine_scalar(), tfb_affine(), tfb_ascending(), tfb_batch_normalization(), tfb_blockwise(), tfb_chain(), tfb_cholesky_outer_product(), tfb_cholesky_to_inv_cholesky(), tfb_correlation_cholesky(), tfb_cumsum(), tfb_discrete_cosine_transform(), tfb_expm1(), tfb_exp(), tfb_ffjord(), tfb_fill_scale_tri_l(), tfb_fill_triangular(), tfb_glow(), tfb_gompertz_cdf(), tfb_gumbel_cdf(), tfb_gumbel(), tfb_identity(), tfb_inline(), tfb_invert(), tfb_iterated_sigmoid_centered(), tfb_kumaraswamy_cdf(), tfb_kumaraswamy(), tfb_masked_autoregressive_default_template(), tfb_masked_autoregressive_flow(), tfb_masked_dense(), tfb_matrix_inverse_tri_l(), tfb_matvec_lu(), tfb_normal_cdf(), tfb_ordered(), tfb_pad(), tfb_permute(), tfb_power_transform(), tfb_rational_quadratic_spline(), tfb_rayleigh_cdf(), tfb_real_nvp_default_template(), tfb_real_nvp(), tfb_reciprocal(), tfb_reshape(), tfb_scale_matvec_diag(), tfb_scale_matvec_linear_operator(), tfb_scale_matvec_lu(), tfb_scale_matvec_tri_l(), tfb_scale_tri_l(), tfb_scale(), tfb_shifted_gompertz_cdf(), tfb_shift(), tfb_sigmoid(), tfb_sinh_arcsinh(), tfb_sinh(), tfb_softmax_centered(), tfb_softplus(), tfb_softsign(), tfb_split(), tfb_square(), tfb_tanh(), tfb_transform_diagonal(), tfb_transpose(), tfb_weibull_cdf(), tfb_weibull()