Gumbel: The Gumbel Distribution

In mistr: Mixture and Composite Distributions

The Gumbel Distribution

Description

Density, distribution function, quantile function and random generation for the Gumbel distribution with location and scale parameters.

Usage

dgumbel(x, loc, scale, log = FALSE)

pgumbel(q, loc, scale, lower.tail = TRUE, log.p = FALSE)

qgumbel(p, loc, scale, lower.tail = TRUE, log.p = FALSE)

rgumbel(n, loc, scale)

Arguments

x, q	vector of quantiles.
loc	location parameter.
scale	scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p), default: FALSE.
lower.tail	logical; if TRUE, probabilities are P[X ≤ x] otherwise, P[X > x], default: TRUE.
p	vector of probabilities.
n	number of observations.

Details

The Gumbel distribution function with location parameter μ and scale parameter β has density given by

f(x)=1/β e^-(z+e^-z)

, where z=(x-μ)/β. The cumulative distribution function is

F(x)=e^(-e^z)

with z as stated above.

See https://en.wikipedia.org/wiki/Gumbel_distribution for more details.

Value

dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and rgumbel generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

See Also

gumbeldist

Examples

dgumbel(seq(1, 5), 0, 1)
qgumbel(pgumbel(seq(1, 5), 0, 1), 0 ,1)
rgumbel(5, 0, 1)

mistr documentation built on March 7, 2023, 7:42 p.m.