16.4 Scaled Inverse Chi-Square Distribution
16.4.1 Probability Density Function
If \(\nu \in \mathbb{R}^+\) and \(\sigma \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{ScaledInvChiSquare}(y|\nu,\sigma) = \frac{(\nu / 2)^{\nu/2}} {\Gamma(\nu / 2)} \, \sigma^{\nu} \, y^{-(\nu/2 + 1)} \, \exp \! \left( \! - \, \frac{1}{2} \, \nu \, \sigma^2 \, \frac{1}{y} \right) . \]
16.4.2 Sampling Statement
y ~ scaled_inv_chi_square(nu, sigma)
Increment target log probability density with scaled_inv_chi_square_lpdf(y | nu, sigma)
dropping constant additive terms.
16.4.3 Stan Functions
real scaled_inv_chi_square_lpdf(reals y | reals nu, reals sigma)
The log of the scaled inverse Chi-square density of y given degrees of
freedom nu and scale sigma
real scaled_inv_chi_square_cdf(reals y, reals nu, reals sigma)
The scaled inverse Chi-square cumulative distribution function of y
given degrees of freedom nu and scale sigma
real scaled_inv_chi_square_lcdf(reals y | reals nu, reals sigma)
The log of the scaled inverse Chi-square cumulative distribution
function of y given degrees of freedom nu and scale sigma
real scaled_inv_chi_square_lccdf(reals y | reals nu, reals sigma)
The log of the scaled inverse Chi-square complementary cumulative
distribution function of y given degrees of freedom nu and scale sigma
R scaled_inv_chi_square_rng(reals nu, reals sigma)
Generate a scaled inverse Chi-squared variate with degrees of freedom
nu 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.