18.2 Chi-square distribution
18.2.1 Probability density function
If \(\nu \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{ChiSquare}(y|\nu) = \frac{2^{-\nu/2}} {\Gamma(\nu / 2)} \, y^{\nu/2 - 1} \, \exp \! \left( -\, \frac{1}{2} \, y \right) . \]
18.2.2 Sampling statement
y ~ chi_square(nu)
Increment target log probability density with chi_square_lupdf(y | nu).
Available since 2.0
18.2.3 Stan functions
real chi_square_lpdf(reals y | reals nu)
The log of the Chi-square density of y given degrees of freedom nu
Available since 2.12
real chi_square_lupdf(reals y | reals nu)
The log of the Chi-square density of y given degrees of freedom nu
dropping constant additive terms
Available since 2.25
real chi_square_cdf(reals y, reals nu)
The Chi-square cumulative distribution function of y given degrees of
freedom nu
Available since 2.0
real chi_square_lcdf(reals y | reals nu)
The log of the Chi-square cumulative distribution function of y given
degrees of freedom nu
Available since 2.12
real chi_square_lccdf(reals y | reals nu)
The log of the complementary Chi-square cumulative distribution
function of y given degrees of freedom nu
Available since 2.12
R chi_square_rng(reals nu)
Generate a Chi-square 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.
Available since 2.18