pgumbel: PDF of the Gumbel Distribution
In DAMisc: Dave Armstrong's Miscellaneous Functions

Description Usage Arguments Details Value Author(s)

Returns the PDF of the Gumbel distribution.

1	pgumbel(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

`q`	Vector of quantiles
`location`	The location parameter, mu. This is not the mean of the Gumbel distribution.
`scale`	The scale parameter sigma.
`lower.tail`	Logical, whether lower, if `TRUE` or upper, if `FALSE`, tail probabilities should be returned.
`log.p`	Logical, if `TRUE` probabilities are given in their log.

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 ≤ft( - \exp ≤ft[ - \frac{y-μ}{σ} \right]\right)

where -∞<y<∞, -∞<μ<∞and σ>0. Its mean is

μ - σ * γ

and its variance is

σ^2 * π^2 / 6

where gamma is Euler's constant (which can be obtained as -digamma(1)).

A vector of probabilities

Thomas Yee

DAMisc documentation built on Jan. 12, 2022, 1:07 a.m.