Gumbel {powdist}

The Gumbel Distribution

Description

Density, distribution function, quantile function and random generation for the Gumbel distribution with parameters mu and sigma.

Usage

dgumbel(x, mu = 0, sigma = 1, log = FALSE)

pgumbel(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

qgumbel(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rgumbel(n, mu = 0, sigma = 1)

Arguments

x, q

vector of quantiles.

mu, sigma

location and scale parameters.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X \le x ], otherwise, P[X > x].

p

vector of probabilities.

n

number of observations.

Details

The Gumbel distribution has density

f(x)=\left[\frac{1}{\sigma}e^{\left(-\frac{x-\mu}{\sigma}\right)-e^{\left(-\frac{x-\mu}{\sigma}\right)}}\right],

where -\infty<\mu<\infty is the location paramether and \sigma^2>0 is the scale parameter.

Examples

dgumbel(1, 3, 4)
pgumbel(1, 3, 4)
qgumbel(0.2, 3, 4)
rgumbel(5, 3, 4)