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18.9 Gumbel distribution

18.9.1 Probability density function

If μR and βR+, then for yR, Gumbel(y|μ,β)=1β exp(yμβexp(yμβ)).

18.9.2 Sampling statement

y ~ gumbel(mu, beta)

Increment target log probability density with gumbel_lupdf(y | mu, beta).
Available since 2.0

18.9.3 Stan functions

real gumbel_lpdf(reals y | reals mu, reals beta)
The log of the gumbel density of y given location mu and scale beta
Available since 2.12

real gumbel_lupdf(reals y | reals mu, reals beta)
The log of the gumbel density of y given location mu and scale beta dropping constant additive terms
Available since 2.25

real gumbel_cdf(reals y, reals mu, reals beta)
The gumbel cumulative distribution function of y given location mu and scale beta
Available since 2.0

real gumbel_lcdf(reals y | reals mu, reals beta)
The log of the gumbel cumulative distribution function of y given location mu and scale beta
Available since 2.12

real gumbel_lccdf(reals y | reals mu, reals beta)
The log of the gumbel complementary cumulative distribution function of y given location mu and scale beta
Available since 2.12

R gumbel_rng(reals mu, reals beta)
Generate a gumbel variate with location mu and scale beta; 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