tfd_johnson_s_u: Johnson's SU-distribution.
In tfprobability: Interface to 'TensorFlow Probability'

tfd_johnson_s_u

R Documentation

Johnson's SU-distribution.

Description

This distribution has parameters: shape parameters skewness and tailweight, location loc, and scale.

Usage

tfd_johnson_s_u(
  skewness,
  tailweight,
  loc,
  scale,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = NULL
)

Arguments

`skewness`	Floating-point `Tensor`. Skewness of the distribution(s).
`tailweight`	Floating-point `Tensor`. Tail weight of the distribution(s). `tailweight` must contain only positive values.
`loc`	Floating-point `Tensor`. The mean(s) of the distribution(s).
`scale`	Floating-point `Tensor`. The scaling factor(s) for the distribution(s). Note that `scale` is not technically the standard deviation of this distribution but has semantics more similar to standard deviation than variance.
`validate_args`	Logical, default FALSE. When TRUE distribution parameters are checked for validity despite possibly degrading runtime performance. When FALSE invalid inputs may silently render incorrect outputs. Default value: FALSE.
`allow_nan_stats`	Logical, default TRUE. When TRUE, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When FALSE, an exception is raised if one or more of the statistic's batch members are undefined.
`name`	name prefixed to Ops created by this class.

Details

Mathematical details

The probability density function (pdf) is,

pdf(x; s, t, xi, sigma) = exp(-0.5 (s + t arcsinh(y))**2) / Z
  where,
    s = skewness
    t = tailweight
    y = (x - xi) / sigma
    Z = sigma sqrt(2 pi) sqrt(1 + y**2) / t

where:

loc = xi,
scale = sigma, and,
Z is the normalization constant. The JohnsonSU distribution is a member of the location-scale family, i.e., it can be constructed as,

X ~ JohnsonSU(skewness, tailweight, loc=0, scale=1)
Y = loc + scale * X

Value

a distribution instance.

Other distributions: tfd_autoregressive(), tfd_batch_reshape(), tfd_bates(), tfd_bernoulli(), tfd_beta_binomial(), tfd_beta(), tfd_binomial(), tfd_categorical(), tfd_cauchy(), tfd_chi2(), tfd_chi(), tfd_cholesky_lkj(), tfd_continuous_bernoulli(), tfd_deterministic(), tfd_dirichlet_multinomial(), tfd_dirichlet(), tfd_empirical(), tfd_exp_gamma(), tfd_exp_inverse_gamma(), tfd_exponential(), tfd_gamma_gamma(), tfd_gamma(), tfd_gaussian_process_regression_model(), tfd_gaussian_process(), tfd_generalized_normal(), tfd_geometric(), tfd_gumbel(), tfd_half_cauchy(), tfd_half_normal(), tfd_hidden_markov_model(), tfd_horseshoe(), tfd_independent(), tfd_inverse_gamma(), tfd_inverse_gaussian(), tfd_joint_distribution_named_auto_batched(), tfd_joint_distribution_named(), tfd_joint_distribution_sequential_auto_batched(), tfd_joint_distribution_sequential(), tfd_kumaraswamy(), tfd_laplace(), tfd_linear_gaussian_state_space_model(), tfd_lkj(), tfd_log_logistic(), tfd_log_normal(), tfd_logistic(), tfd_mixture_same_family(), tfd_mixture(), tfd_multinomial(), tfd_multivariate_normal_diag_plus_low_rank(), tfd_multivariate_normal_diag(), tfd_multivariate_normal_full_covariance(), tfd_multivariate_normal_linear_operator(), tfd_multivariate_normal_tri_l(), tfd_multivariate_student_t_linear_operator(), tfd_negative_binomial(), tfd_normal(), tfd_one_hot_categorical(), tfd_pareto(), tfd_pixel_cnn(), tfd_poisson_log_normal_quadrature_compound(), tfd_poisson(), tfd_power_spherical(), tfd_probit_bernoulli(), tfd_quantized(), tfd_relaxed_bernoulli(), tfd_relaxed_one_hot_categorical(), tfd_sample_distribution(), tfd_sinh_arcsinh(), tfd_skellam(), tfd_spherical_uniform(), tfd_student_t_process(), tfd_student_t(), tfd_transformed_distribution(), tfd_triangular(), tfd_truncated_cauchy(), tfd_truncated_normal(), tfd_uniform(), tfd_variational_gaussian_process(), tfd_vector_diffeomixture(), tfd_vector_exponential_diag(), tfd_vector_exponential_linear_operator(), tfd_vector_laplace_diag(), tfd_vector_laplace_linear_operator(), tfd_vector_sinh_arcsinh_diag(), tfd_von_mises_fisher(), tfd_von_mises(), tfd_weibull(), tfd_wishart_linear_operator(), tfd_wishart_tri_l(), tfd_wishart(), tfd_zipf()