tfb_sinh_arcsinh | R Documentation |
Y = g(X) = Sinh( (Arcsinh(X) + skewness) * tailweight )
For skewness in (-inf, inf)
and tailweight in (0, inf)
, this
transformation is a diffeomorphism of the real line (-inf, inf)
.
The inverse transform is X = g^{-1}(Y) = Sinh( ArcSinh(Y) / tailweight - skewness )
.
The SinhArcsinh transformation of the Normal is described in
Sinh-arcsinh distributions
tfb_sinh_arcsinh( skewness = NULL, tailweight = NULL, validate_args = FALSE, name = "SinhArcsinh" )
skewness |
Skewness parameter. Float-type Tensor. Default is 0 of type float32. |
tailweight |
Tailweight parameter. Positive Tensor of same dtype as skewness and broadcastable shape. Default is 1 of type float32. |
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. |
This Bijector allows a similar transformation of any distribution supported on (-inf, inf)
.
a bijector instance.
If skewness = 0 and tailweight = 1, this transform is the identity.
Positive (negative) skewness leads to positive (negative) skew.
positive skew means, for unimodal X centered at zero, the mode of Y is "tilted" to the right.
positive skew means positive values of Y become more likely, and negative values become less likely.
Larger (smaller) tailweight leads to fatter (thinner) tails.
Fatter tails mean larger values of |Y| become more likely.
If X is a unit Normal, tailweight < 1 leads to a distribution that is "flat" around Y = 0, and a very steep drop-off in the tails.
If X is a unit Normal, tailweight > 1 leads to a distribution more peaked at the mode with heavier tails. To see the argument about the tails, note that for |X| >> 1 and |X| >> (|skewness| * tailweight)tailweight, we have Y approx 0.5 Xtailweight e**(sign(X) skewness * tailweight).
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_lambert_w_tail()
,
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()
,
tfb_softmax_centered()
,
tfb_softplus()
,
tfb_softsign()
,
tfb_split()
,
tfb_square()
,
tfb_tanh()
,
tfb_transform_diagonal()
,
tfb_transpose()
,
tfb_weibull_cdf()
,
tfb_weibull()
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