Generalized Extreme Value Distribution (for maxima)

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Description

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

Usage

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dgev(x,shape=1,scale=1,location=0,log=FALSE)
pgev(q,shape=1,scale=1,location=0,lower.tail=TRUE,log.p=FALSE)
qgev(p,shape=1,scale=1,location=0,lower.tail=TRUE,log.p=FALSE)
rgev(n,shape=1,scale=1,location=0)

Arguments

x,q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

shape

shape parameter.

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].

Details

If X is a random variable distributed according to a generalized extreme value distribution, it has density
f(x) = 1/scale*(1+shape*((x-location)/scale))^(-1/shape-1)*exp(-(1+shape*((x-location)/scale))^(-1/shape))

Value

dgev gives the density, pgev gives the distribution function, qgev gives the quantile function, and rgev generates random deviates.

References

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

Examples

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x <- rgev(1000,-.1,3,100)
hist(x,freq=FALSE,col='gray',border='white')
curve(dgev(x,-.1,3,100),add=TRUE,col='red4',lwd=2)