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17.4 Scaled inverse chi-square distribution

17.4.1 Probability density function

If $\nu \in \mathbb{R}^+$ and $\sigma \in \mathbb{R}^+$, then for $y \in \mathbb{R}^+$, $$\text{ScaledInvChiSquare}(y|\nu,\sigma) = \frac{(\nu / 2)^{\nu/2}} {\Gamma(\nu / 2)} \, \sigma^{\nu} \, y^{-(\nu/2 + 1)} \, \exp \! \left( \! - \, \frac{1}{2} \, \nu \, \sigma^2 \, \frac{1}{y} \right) .$$

17.4.2 Sampling statement

y ~ scaled_inv_chi_square(nu, sigma)

Increment target log probability density with scaled_inv_chi_square_lupdf(y | nu, sigma).

17.4.3 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_lupdf(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 dropping constant additive terms

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.