pgumbel {DAMisc} | R Documentation |
Returns the PDF of the Gumbel distribution.
pgumbel(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
q |
Vector of quantiles |
location |
The location parameter, |
scale |
The scale parameter |
lower.tail |
Logical, whether lower, if |
log.p |
Logical, if |
This code and the details of the help file were taken from the VGAM
package.
The Gumbel distribution is a special case of the generalized extreme value
(GEV) distribution where the shape parameter \xi
= 0. The latter has 3 parameters, so
the Gumbel distribution has two. The Gumbel distribution function is
G(y) = \exp \left( - \exp \left[ - \frac{y-\mu}{\sigma} \right]\right)
where -\infty<y<\infty
, -\infty<\mu<\infty
and \sigma>0
.
Its mean is
\mu - \sigma * \gamma
and its variance is
\sigma^2 * \pi^2 / 6
where \gamma
is Euler's constant (which can be obtained as -digamma(1)
).
A vector of probabilities
Thomas Yee