mistr (version 0.0.2)

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)

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.

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.

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

# NOT RUN {
dgumbel(seq(1, 5), 0, 1)
qgumbel(pgumbel(seq(1, 5), 0, 1), 0 ,1)
rgumbel(5, 0, 1)
# }