25.6 Multivariate Student-t distribution
25.6.1 Probability density function
If K∈N, ν∈R+, μ∈RK, and Σ∈RK×K is symmetric and positive definite, then for y∈RK, MultiStudentT(y|ν,μ,Σ)=1πK/2 1νK/2 Γ((ν+K)/2)Γ(ν/2) 1√|Σ| (1+1ν(y−μ)⊤Σ−1(y−μ))−(ν+K)/2.
25.6.2 Sampling statement
y ~
multi_student_t
(nu, mu, Sigma)
Increment target log probability density with multi_student_t_lupdf(y | nu, mu, Sigma)
.
Available since 2.0
25.6.3 Stan functions
real
multi_student_t_lpdf
(vectors y | real nu, vectors mu, matrix Sigma)
The log of the multivariate Student-t density of vector(s) y given
degrees of freedom nu, location vector(s) mu, and scale matrix Sigma
Available since 2.18
real
multi_student_t_lupdf
(vectors y | real nu, vectors mu, matrix Sigma)
The log of the multivariate Student-t density of vector(s) y given
degrees of freedom nu, location vector(s) mu, and scale matrix Sigma
dropping constant additive terms
Available since 2.25
real
multi_student_t_lpdf
(vectors y | real nu, row_vectors mu, matrix Sigma)
The log of the multivariate Student-t density of vector(s) y given
degrees of freedom nu, location row vector(s) mu, and scale matrix
Sigma
Available since 2.18
real
multi_student_t_lupdf
(vectors y | real nu, row_vectors mu, matrix Sigma)
The log of the multivariate Student-t density of vector(s) y given
degrees of freedom nu, location row vector(s) mu, and scale matrix
Sigma dropping constant additive terms
Available since 2.25
real
multi_student_t_lpdf
(row_vectors y | real nu, vectors mu, matrix Sigma)
The log of the multivariate Student-t density of row vector(s) y
given degrees of freedom nu, location vector(s) mu, and scale matrix
Sigma
Available since 2.18
real
multi_student_t_lupdf
(row_vectors y | real nu, vectors mu, matrix Sigma)
The log of the multivariate Student-t density of row vector(s) y
given degrees of freedom nu, location vector(s) mu, and scale matrix
Sigma dropping constant additive terms
Available since 2.25
real
multi_student_t_lpdf
(row_vectors y | real nu, row_vectors mu, matrix Sigma)
The log of the multivariate Student-t density of row vector(s) y
given degrees of freedom nu, location row vector(s) mu, and scale
matrix Sigma
Available since 2.18
real
multi_student_t_lupdf
(row_vectors y | real nu, row_vectors mu, matrix Sigma)
The log of the multivariate Student-t density of row vector(s) y
given degrees of freedom nu, location row vector(s) mu, and scale
matrix Sigma dropping constant additive terms
Available since 2.25
vector
multi_student_t_rng
(real nu, vector mu, matrix Sigma)
Generate a multivariate Student-t variate with degrees of freedom
nu, location mu, and scale matrix Sigma; may only be used in transformed data
and generated quantities blocks
Available since 2.0
vector
multi_student_t_rng
(real nu, row_vector mu, matrix Sigma)
Generate a multivariate Student-t variate with degrees of freedom
nu, location mu, and scale matrix Sigma; may only be used in transformed data
and generated quantities blocks
Available since 2.18
vectors
multi_student_t_rng
(real nu, vectors mu, matrix Sigma)
Generate an array of multivariate Student-t variates with degrees of
freedom nu, locations mu, and scale matrix Sigma; may only be used in
transformed data and generated quantities blocks
Available since 2.18
vectors
multi_student_t_rng
(real nu, row_vectors mu, matrix Sigma)
Generate an array of multivariate Student-t variates with degrees of
freedom nu, locations mu, and scale matrix Sigma; may only be used in
transformed data andgenerated quantities blocks
Available since 2.18