mistr (version 0.0.6)

Gumbel: 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)

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.

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 \(P[X \le x]\) otherwise, \(P[X > x]\), default: TRUE.

p

vector of probabilities.

n

number of observations.

Details

The Gumbel distribution function with location parameter \(\mu\) and scale parameter \(\beta\) has density given by $$f(x)=1/\beta e^-(z+e^-z)$$, where \(z=(x-\mu)/\beta\). 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.

See Also

gumbeldist

Examples

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