17.5 Student-t distribution
17.5.1 Probability density function
If ν∈R+, μ∈R, and σ∈R+, then for y∈R, StudentT(y|ν,μ,σ)=Γ((ν+1)/2)Γ(ν/2) 1√νπ σ (1+1ν(y−μσ)2)−(ν+1)/2.
17.5.2 Sampling statement
y ~
student_t
(nu, mu, sigma)
Increment target log probability density with student_t_lupdf(y | nu, mu, sigma)
.
Available since 2.0
17.5.3 Stan functions
real
student_t_lpdf
(reals y | reals nu, reals mu, reals sigma)
The log of the Student-t density of y given degrees of freedom nu,
location mu, and scale sigma
Available since 2.12
real
student_t_lupdf
(reals y | reals nu, reals mu, reals sigma)
The log of the Student-t density of y given degrees of freedom nu,
location mu, and scale sigma dropping constant additive terms
Available since 2.25
real
student_t_cdf
(reals y, reals nu, reals mu, reals sigma)
The Student-t cumulative distribution function of y given degrees of
freedom nu, location mu, and scale sigma
Available since 2.0
real
student_t_lcdf
(reals y | reals nu, reals mu, reals sigma)
The log of the Student-t cumulative distribution function of y given
degrees of freedom nu, location mu, and scale sigma
Available since 2.12
real
student_t_lccdf
(reals y | reals nu, reals mu, reals sigma)
The log of the Student-t complementary cumulative distribution
function of y given degrees of freedom nu, location mu, and scale
sigma
Available since 2.12
R
student_t_rng
(reals nu, reals mu, reals sigma)
Generate a Student-t variate with degrees of freedom nu, location
mu, and scale sigma; may only be used in transformed data and generated
quantities blocks. For a description of argument and return types, see section
vectorized PRNG functions.
Available since 2.18