20.9 Frechet distribution
20.9.1 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 \(Y^{-1} \propto \text{Weibull}(\alpha,\sigma^{-1})\).
20.9.2 Sampling statement
y ~ frechet(alpha, sigma)
Increment target log probability density with frechet_lupdf(y | alpha, sigma).
Available since 2.5
20.9.3 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
Available since 2.12
real frechet_lupdf(reals y | reals alpha, reals sigma)
The log of the Frechet density of y given shape alpha and scale sigma
dropping constant additive terms
Available since 2.25
real frechet_cdf(reals y, reals alpha, reals sigma)
The Frechet cumulative distribution function of y given shape alpha
and scale sigma
Available since 2.5
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
Available since 2.12
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
Available since 2.12
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.
Available since 2.18