pgumbel {DAMisc} R Documentation

## PDF of the Gumbel Distribution

### Description

Returns the PDF of the Gumbel distribution.

### Usage

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


### Arguments

 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.

### Details

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<\inftyand \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)).

### Value

A vector of probabilities

### Author(s)

Thomas Yee

[Package DAMisc version 1.7.2 Index]