18.7 Inverse gamma Distribution
18.7.1 Probability density function
If \(\alpha \in \mathbb{R}^+\) and \(\beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{InvGamma}(y|\alpha,\beta) = \frac{\beta^{\alpha}} {\Gamma(\alpha)} \ y^{-(\alpha + 1)} \, \exp \! \left( \! - \beta \, \frac{1}{y} \right) . \]
18.7.2 Sampling statement
y ~ inv_gamma(alpha, beta)
Increment target log probability density with inv_gamma_lupdf(y | alpha, beta).
Available since 2.0
18.7.3 Stan functions
real inv_gamma_lpdf(reals y | reals alpha, reals beta)
The log of the inverse gamma density of y given shape alpha and scale
beta
Available since 2.12
real inv_gamma_lupdf(reals y | reals alpha, reals beta)
The log of the inverse gamma density of y given shape alpha and scale
beta dropping constant additive terms
Available since 2.25
real inv_gamma_cdf(reals y, reals alpha, reals beta)
The inverse gamma cumulative distribution function of y given shape
alpha and scale beta
Available since 2.0
real inv_gamma_lcdf(reals y | reals alpha, reals beta)
The log of the inverse gamma cumulative distribution function of y
given shape alpha and scale beta
Available since 2.12
real inv_gamma_lccdf(reals y | reals alpha, reals beta)
The log of the inverse gamma complementary cumulative distribution
function of y given shape alpha and scale beta
Available since 2.12
R inv_gamma_rng(reals alpha, reals beta)
Generate an inverse gamma variate with shape alpha and scale beta; 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