GEV: Generalized Extreme Value Distribution (for maxima)

In FAdist: Distributions that are Sometimes Used in Hydrology

Generalized Extreme Value Distribution (for maxima)

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

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

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)

FAdist documentation built on March 18, 2022, 5:24 p.m.