17.3 Inverse Chi-Square Distribution
17.3.1 Probability Density Function
If \(\nu \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{InvChiSquare}(y \, | \, \nu) = \frac{2^{-\nu/2}} {\Gamma(\nu / 2)} \, y^{-\nu/2 - 1} \, \exp\! \left( \! - \, \frac{1}{2} \, \frac{1}{y} \right) . \]
17.3.2 Sampling Statement
y ~ inv_chi_square(nu)
Increment target log probability density with inv_chi_square_lupdf(y | nu).
17.3.3 Stan Functions
real inv_chi_square_lpdf(reals y | reals nu)
The log of the inverse Chi-square density of y given degrees of
freedom nu
real inv_chi_square_lupdf(reals y | reals nu)
The log of the inverse Chi-square density of y given degrees of
freedom nu dropping constant additive terms
real inv_chi_square_cdf(reals y, reals nu)
The inverse Chi-squared cumulative distribution function of y given
degrees of freedom nu
real inv_chi_square_lcdf(reals y | reals nu)
The log of the inverse Chi-squared cumulative distribution function of
y given degrees of freedom nu
real inv_chi_square_lccdf(reals y | reals nu)
The log of the inverse Chi-squared complementary cumulative
distribution function of y given degrees of freedom nu
R inv_chi_square_rng(reals nu)
Generate an inverse Chi-squared variate with degrees of freedom nu;
may only be used in transformed data and generated quantities blocks.
For a description of argument and return types, see section
vectorized PRNG functions.