This is an old version, view current version.

25.6 Multivariate Student-t distribution

25.6.1 Probability density function

If KN, νR+, μRK, and ΣRK×K is symmetric and positive definite, then for yRK, MultiStudentT(y|ν,μ,Σ)=1πK/2 1νK/2 Γ((ν+K)/2)Γ(ν/2) 1|Σ| (1+1ν(yμ)Σ1(yμ))(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 transfomed 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