tfd_multivariate_student_t_linear_operator {tfprobability} | R Documentation |
Multivariate Student's t-distribution on R^k
Description
Mathematical Details
Usage
tfd_multivariate_student_t_linear_operator(
df,
loc,
scale,
validate_args = FALSE,
allow_nan_stats = TRUE,
name = "MultivariateStudentTLinearOperator"
)
Arguments
df |
A positive floating-point |
loc |
Floating-point |
scale |
Instance of |
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
The probability density function (pdf) is,
pdf(x; df, loc, Sigma) = (1 + ||y||**2 / df)**(-0.5 (df + k)) / Z where, y = inv(Sigma) (x - loc) Z = abs(det(Sigma)) sqrt(df pi)**k Gamma(0.5 df) / Gamma(0.5 (df + k))
where:
-
df
is a positive scalar. -
loc
is a vector inR^k
, -
Sigma
is a positive definiteshape
matrix inR^{k x k}
, parameterized asscale @ scale.T
in this class, -
Z
denotes the normalization constant, and, -
||y||**2
denotes the squared Euclidean norm ofy
.
The Multivariate Student's t-distribution distribution is a member of the location-scale family, i.e., it can be constructed as,
X ~ MultivariateT(loc=0, scale=1) # Identity scale, zero shift. Y = scale @ X + loc
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_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()