FAdist (version 2.4)

GUMBEL: Gumbel Distribution (for maxima)

Description

Density, distribution function, quantile function and random generation for the Gumbel distribution (for maxima) with scale and location parameters equal to scale and location, respectively.

Usage

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

Arguments

x,q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

scale

scale parameter.

location

location parameter.

log,log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Value

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

Details

If X is a random variable distributed according to a Gumbel distribution, it has density

f(x) = 1/scale*exp(-(x-location)/scale-exp(-(x-location)/scale))

References

Coles, S. (2001) An introduction to statistical modeling of extreme values. Springer

Examples

# NOT RUN {
x <- rgumbel(1000,3,100)
hist(x,freq=FALSE,col='gray',border='white')
curve(dgumbel(x,3,100),add=TRUE,col='red4',lwd=2)
# }