tfd_zipf: Zipf distribution

In tfprobability: Interface to 'TensorFlow Probability'

Zipf distribution

Description

The Zipf distribution is parameterized by a power parameter.

Usage

tfd_zipf(
  power,
  dtype = tf$int32,
  interpolate_nondiscrete = TRUE,
  sample_maximum_iterations = 100,
  validate_args = FALSE,
  allow_nan_stats = FALSE,
  name = "Zipf"
)

Arguments

power	Float like Tensor representing the power parameter. Must be strictly greater than 1.
dtype	The dtype of Tensor returned by sample. Default value: tf$int32.
interpolate_nondiscrete	Logical. When FALSE, log_prob returns -inf (and prob returns 0) for non-integer inputs. When TRUE, log_prob evaluates the continuous function -power log(k) - log(zeta(power)) , which matches the Zipf pmf at integer arguments k (note that this function is not itself a normalized probability log-density). Default value: TRUE.
sample_maximum_iterations	Maximum number of iterations of allowable iterations in sample. When validate_args=TRUE, samples which fail to reach convergence (subject to this cap) are masked out with self$dtype$min or nan depending on self$dtype$is_integer. Default value: 100.
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	Default value: FALSE.
name	name prefixed to Ops created by this class.

Details

Mathematical Details The probability mass function (pmf) is,

pmf(k; alpha, k >= 0) = (k^(-alpha)) / Z
Z = zeta(alpha).

where power = alpha and Z is the normalization constant. zeta is the Riemann zeta function. Note that gradients with respect to the power parameter are not supported in the current implementation.

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_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()

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