evd: gumbel – R documentation

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gumbel

The Gumbel Distribution

Description

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

Usage

dgumbel(x, loc=0, scale=1, log = FALSE) 
pgumbel(q, loc=0, scale=1, lower.tail = TRUE) 
qgumbel(p, loc=0, scale=1, lower.tail = TRUE)
rgumbel(n, loc=0, scale=1)

Arguments

`x, q`	Vector of quantiles.
`p`	Vector of probabilities.
`n`	Number of observations.
`loc, scale`	Location and scale parameters (can be given as vectors).
`log`	Logical; if `TRUE`, the log density is returned.
`lower.tail`	Logical; if `TRUE` (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The Gumbel distribution function with parameters \code{loc} = a and \code{scale} = b is

G(x) = exp{-exp[-(z-a)/b]}

for all real z, where b > 0.

Value

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

Examples

dgumbel(-1:2, -1, 0.5)
pgumbel(-1:2, -1, 0.5)
qgumbel(seq(0.9, 0.6, -0.1), 2, 0.5)
rgumbel(6, -1, 0.5)
p <- (1:9)/10
pgumbel(qgumbel(p, -1, 2), -1, 2)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

evd

Functions for Extreme Value Distributions

v2.3-3

GPL-3

Authors

Alec Stephenson. Function fbvpot by Chris Ferro.

Initial release

2018-04-25