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 transformed data and generated quantities blocks. For a description of argument and return types, see section vectorized PRNG functions.