Gumbel distribution — gumbel • RTMBdist

Density, distribution function, quantile function, and random generation for the Gumbel distribution.

Usage

dgumbel(x, location = 0, scale = 1, log = FALSE)

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

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

rgumbel(n, location = 0, scale = 1)

Arguments

x, q: vector of quantiles
location: location parameter
scale: scale parameter, must be positive.
log, log.p: logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).
lower.tail: logical; if TRUE, probabilities are \(P[X <= x]\), otherwise, \(P[X > x]\).
p: vector of probabilities
n: number of random values to return

Value

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

Details

This implementation of dgumbel allows for automatic differentiation with RTMB.

Examples

x <- rgumbel(1, 0.5, 2)
d <- dgumbel(x, 0.5, 2)
p <- pgumbel(x, 0.5, 2)
q <- qgumbel(p, 0.5, 2)