18.9 Gumbel distribution
18.9.1 Probability density function
If μ∈R and β∈R+, then for y∈R, Gumbel(y|μ,β)=1β exp(−y−μβ−exp(−y−μβ)).
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