The Beta distribution is defined over the (0, 1) interval using parameters concentration1 (aka "alpha") and concentration0 (aka "beta").

  concentration1 = NULL,
  concentration0 = NULL,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "Beta"



Positive floating-point Tensor indicating mean number of successes; aka "alpha". Implies self$dtype and self$batch_shape, i.e., concentration1$shape = [N1, N2, ..., Nm] = self$batch_shape.


Positive floating-point Tensor indicating mean number of failures; aka "beta". Otherwise has same semantics as concentration1.


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.


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 prefixed to Ops created by this class.


a distribution instance.


Mathematical Details

The probability density function (pdf) is,

pdf(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z
Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta)


  • concentration1 = alpha,

  • concentration0 = beta,

  • Z is the normalization constant, and,

  • Gamma is the gamma function. The concentration parameters represent mean total counts of a 1 or a 0, i.e.,

concentration1 = alpha = mean * total_concentration
concentration0 = beta  = (1. - mean) * total_concentration

where mean in (0, 1) and total_concentration is a positive real number representing a mean total_count = concentration1 + concentration0. Distribution parameters are automatically broadcast in all functions; see examples for details. Warning: The samples can be zero due to finite precision. This happens more often when some of the concentrations are very small. Make sure to round the samples to np$finfo(dtype)$tiny before computing the density. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in the paper Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit Reparameterization Gradients, 2018

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_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(), tfd_zipf()