Compute Y = g(X) = (1 - exp(-rate * X)) * exp(-c * exp(-rate * X))

This bijector maps inputs from [-inf, inf] to [0, inf]. The inverse of the bijector applied to a uniform random variable X ~ U(0, 1) gives back a random variable with the Shifted Gompertz distribution:

Y ~ ShiftedGompertzCDF(concentration, rate)
pdf(y; c, r) = r * exp(-r * y - exp(-r * y) / c) * (1 + (1 - exp(-r * y)) / c)

tfb_shifted_gompertz_cdf(
  concentration,
  rate,
  validate_args = FALSE,
  name = "shifted_gompertz_cdf"
)

Arguments

concentration	Positive Float-like Tensor that is the same dtype and is broadcastable with concentration. This is c in Y = g(X) = (1 - exp(-rate * X)) * exp(-c * exp(-rate * X)).
rate	Positive Float-like Tensor that is the same dtype and is broadcastable with concentration. This is rate in Y = g(X) = (1 - exp(-rate * X)) * exp(-c * exp(-rate * X)).
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

Note: Even though this is called ShiftedGompertzCDF, when applied to the Uniform distribution, this is not the same as applying a GompertzCDF with a Shift bijector (i.e. the Shifted Gompertz distribution is not the same as a Gompertz distribution with a location parameter).

Note: Because the Shifted Gompertz distribution concentrates its mass close to zero, for larger rates or larger concentrations, bijector$forward will quickly saturate to 1.

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_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_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()