16.9 Frechet Distribution
16.9.1 Probability Density Function
If α∈R+ and σ∈R+, then for y∈R+, Frechet(y|α,σ)=ασ(yσ)−α−1exp(−(yσ)−α).
Note that if Y∝Frechet(α,σ), then Y−1∝Weibull(α,σ−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.