16.9 Frechet Distribution
16.9.1 Probability Density Function
If \(\alpha \in \mathbb{R}^+\) and \(\sigma \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{Frechet}(y|\alpha,\sigma) = \frac{\alpha}{\sigma} \, \left( \frac{y}{\sigma} \right)^{-\alpha - 1} \, \exp \! \left( \! - \left( \frac{y}{\sigma} \right)^{-\alpha} \right) . \]
Note that if \(Y \propto \text{Frechet}(\alpha,\sigma)\), then \(Y^{-1} \propto \text{Weibull}(\alpha,\sigma^{-1})\).
16.9.2 Sampling Statement
y ~ frechet(alpha, sigma)
Increment target log probability density with frechet_lpdf( y | alpha, sigma)
dropping constant additive terms.
16.9.3 Stan Functions
real frechet_lpdf(reals y | reals alpha, reals sigma)
The log of the Frechet density of y given shape alpha and scale sigma
real frechet_cdf(reals y, reals alpha, reals sigma)
The Frechet cumulative distribution function of y given shape alpha
and scale sigma
real frechet_lcdf(reals y | reals alpha, reals sigma)
The log of the Frechet cumulative distribution function of y given
shape alpha and scale sigma
real frechet_lccdf(reals y | reals alpha, reals sigma)
The log of the Frechet complementary cumulative distribution function
of y given shape alpha and scale sigma
R frechet_rng(reals alpha, reals sigma)
Generate a Frechet variate with shape alpha 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.