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16.9 Frechet Distribution

16.9.1 Probability Density Function

If αR+ and σR+, then for yR+, Frechet(y|α,σ)=ασ(yσ)α1exp((yσ)α).

Note that if YFrechet(α,σ), then Y1Weibull(α,σ1).

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.