Gumbel: The Gumbel Distribution

In powdist: Power and Reversal Power Distributions

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 ≤ x ], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

The Gumbel distribution has density

f(x)=(1/σ)exp(-(x-μ)/σ-exp(-(x-μ)/σ)),

where -∞<μ<∞ is the location paramether and σ^2>0 is the scale parameter.

Examples

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

Example output

[1] 0.07926048
[1] 0.1922956
[1] 1.09646
[1]  6.3854587  3.7480653 10.4243566  8.0340240  0.1384547

powdist documentation built on May 1, 2019, 10:11 p.m.