tfd_inverse_gaussian: Inverse Gaussian distribution

In tfprobability: Interface to 'TensorFlow Probability'

Inverse Gaussian distribution

Description

The inverse Gaussian distribution is parameterized by a loc and a concentration parameter. It's also known as the Wald distribution. Some, e.g., the Python scipy package, refer to the special case when loc is 1 as the Wald distribution.

Usage

tfd_inverse_gaussian(
  loc,
  concentration,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "InverseGaussian"
)

Arguments

loc	Floating-point Tensor, the loc params. Must contain only positive values.
concentration	Floating-point Tensor, the concentration params. Must contain only positive values.
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

The "inverse" in the name does not refer to the distribution associated to the multiplicative inverse of a random variable. Rather, the cumulant generating function of this distribution is the inverse to that of a Gaussian random variable.

Mathematical Details

The probability density function (pdf) is,

pdf(x; mu, lambda) = [lambda / (2 pi x ** 3)] ** 0.5
exp{-lambda(x - mu) ** 2 / (2 mu ** 2 x)}

where

• loc = mu

• concentration = lambda.

The support of the distribution is defined on (0, infinity). Mapping to R and Python scipy's parameterization:

• R: statmod::invgauss

• mean = loc

• shape = concentration

• dispersion = 1 / concentration. Used only if shape is NULL.

• Python: scipy.stats.invgauss

• mu = loc / concentration

• scale = concentration

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_generalized_normal(), tfd_geometric(), tfd_gumbel(), tfd_half_cauchy(), tfd_half_normal(), tfd_hidden_markov_model(), tfd_horseshoe(), tfd_independent(), tfd_inverse_gamma(), 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.