Mathematical details

tfd_normal(loc, scale, validate_args = FALSE, allow_nan_stats = TRUE,
  name = "Normal")

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.

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.

Value

a distribution instance.

Details

The probability density function (pdf) is,

pdf(x; mu, sigma) = exp(-0.5 (x - mu)**2 / sigma**2) / Z
Z = (2 pi sigma**2)**0.5

where loc = mu is the mean, scale = sigma is the std. deviation, and, Z is the normalization constant. The Normal distribution is a member of the location-scale family, i.e., it can be constructed as,

X ~ Normal(loc=0, scale=1)
Y = loc + scale * X

See also

For usage examples see e.g. tfd_sample(), tfd_log_prob(), tfd_mean().

Other distributions: tfd_autoregressive, tfd_batch_reshape, tfd_bernoulli, tfd_beta, tfd_binomial, tfd_categorical, tfd_cauchy, tfd_chi2, tfd_chi, tfd_cholesky_lkj, tfd_deterministic, tfd_dirichlet_multinomial, tfd_dirichlet, tfd_empirical, tfd_exponential, tfd_gamma_gamma, tfd_gamma, tfd_gaussian_process_regression_model, tfd_gaussian_process, 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_joint_distribution_named, tfd_joint_distribution_sequential, tfd_kumaraswamy, tfd_laplace, tfd_linear_gaussian_state_space_model, tfd_lkj, 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_one_hot_categorical, tfd_pareto, tfd_pixel_cnn, tfd_poisson_log_normal_quadrature_compound, tfd_poisson, tfd_probit_bernoulli, tfd_quantized, tfd_relaxed_bernoulli, tfd_relaxed_one_hot_categorical, tfd_sample_distribution, tfd_sinh_arcsinh, 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_wishart_linear_operator, tfd_wishart_tri_l, tfd_wishart, tfd_zipf