tfd_generalized_normal: The Generalized Normal distribution.

In tfprobability: Interface to 'TensorFlow Probability'

The Generalized Normal distribution.

Description

The Generalized Normal (or Generalized Gaussian) generalizes the Normal distribution with an additional shape parameter. It is parameterized by location loc, scale scale and shape power.

Usage

tfd_generalized_normal(
  loc,
  scale,
  power,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "GeneralizedNormal"
)

Arguments

loc	Floating point tensor; the means of the distribution(s).
scale	Floating point tensor; the scale of the distribution(s). Must contain only positive values.
power	Floating point tensor; the shape parameter of the distribution(s). Must contain only positive values. loc, scale and power must have compatible shapes for broadcasting.
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; loc, scale, power) = 1 / (2 * scale * Gamma(1 + 1 / power)) *
  exp(-(|x - loc| / scale) ^ power)

where loc is the mean, scale is the scale, and, power is the shape parameter. If the power is above two, the distribution becomes platykurtic. A power equal to two results in a Normal distribution. A power smaller than two produces a leptokurtic (heavy-tailed) distribution. Mean and scale behave the same way as in the equivalent Normal distribution.

See https://en.wikipedia.org/w/index.php?title=Generalized_normal_distribution&oldid=954254464 for the definitions used here, including CDF, variance and entropy. See https://sccn.ucsd.edu/wiki/Generalized_Gaussian_Probability_Density_Function for the sampling method used here.

Value

a distribution instance.

See Also

For usage examples see e.g. tfd_sample(), tfd_log_prob(), tfd_mean().

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_geometric(), tfd_gumbel(), tfd_half_cauchy(), tfd_half_normal(), tfd_hidden_markov_model(), tfd_horseshoe(), tfd_independent(), tfd_inverse_gamma(), tfd_inverse_gaussian(), tfd_johnson_s_u(), 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()

tfprobability documentation built on Sept. 1, 2022, 5:07 p.m.