R: The Truncated Cauchy distribution.

tfd_truncated_cauchy {tfprobability}

R Documentation

The Truncated Cauchy distribution.

Description

The truncated Cauchy is a Cauchy distribution bounded between low and high (the pdf is 0 outside these bounds and renormalized). Samples from this distribution are differentiable with respect to loc and scale, but not with respect to the bounds low and high.

Usage

tfd_truncated_cauchy(
  loc,
  scale,
  low,
  high,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "TruncatedCauchy"
)

Arguments

`loc`	Floating point tensor; the modes of the corresponding non-truncated Cauchy distribution(s).
`scale`	Floating point tensor; the scales of the distribution(s). Must contain only positive values.
`low`	`float` `Tensor` representing lower bound of the distribution's support. Must be such that `low < high`.
`high`	`float` `Tensor` representing upper bound of the distribution's support. Must be such that `low < high`.
`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) of this distribution is:

pdf(x; loc, scale, low, high) =
    { 1 / (pi * scale * (1 + z**2) * A) for low <= x <= high
    { 0                                 otherwise
    where
        z = (x - loc) / scale
        A = CauchyCDF((high - loc) / scale) - CauchyCDF((low - loc) / scale)

where CauchyCDF is the cumulative density function of the Cauchy distribution with 0 mean and unit variance. This is a scalar distribution so the event shape is always scalar and the dimensions of the parameters define the batch_shape.

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_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_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()