16.7 Inverse Gamma Distribution
16.7.1 Probability Density Function
If \(\alpha \in \mathbb{R}^+\) and \(\beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{InvGamma}(y|\alpha,\beta) = \frac{\beta^{\alpha}} {\Gamma(\alpha)} \ y^{-(\alpha + 1)} \, \exp \! \left( \! - \beta \, \frac{1}{y} \right) . \]
16.7.2 Sampling Statement
y ~ inv_gamma(alpha, beta)
Increment target log probability density with inv_gamma_lpdf( y | alpha, beta)
dropping constant additive terms.
16.7.3 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
real inv_gamma_cdf(reals y, reals alpha, reals beta)
The inverse gamma cumulative distribution function of y given shape
alpha and scale beta
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
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
R inv_gamma_rng(reals alpha, reals beta)
Generate an inverse gamma variate with shape alpha and scale beta; may
only be used in generated quantities block. For a description of
argument and return types, see section vectorized PRNG functions.