R: Truncated Normal distribution

tfd_truncated_normal {tfprobability}

R Documentation

Truncated Normal distribution

Description

The truncated normal is a normal 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, scale as well as the bounds, low and high, i.e., this implementation is fully reparameterizeable. For more details, see here.

Usage

tfd_truncated_normal(
  loc,
  scale,
  low,
  high,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "TruncatedNormal"
)

Arguments

`loc`	Floating point tensor; the means of the distribution(s).
`scale`	loating point tensor; the stddevs 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) =
  { (2 pi)**(-0.5) exp(-0.5 y**2) / (scale * z)} for low <= x <= high
  { 0 }                                  otherwise
y = (x - loc)/scale
z = NormalCDF((high - loc) / scale) - NormalCDF((lower - loc) / scale)

where:

NormalCDF is the cumulative density function of the Normal 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 defined 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_cauchy(), 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()