gevUC {VGAM}R Documentation

The Generalized Extreme Value Distribution

Description

Density, distribution function, quantile function and random generation for the generalized extreme value distribution (GEV) with location parameter location, scale parameter scale and shape parameter shape.

Usage

dgev(x, location=0, scale=1, shape=0)
pgev(q, location=0, scale=1, shape=0)
qgev(p, location=0, scale=1, shape=0)
rgev(n, location=0, scale=1, shape=0)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. Positive integer of length 1.
location the location parameter mu.
scale the scale parameter sigma. Must consist of positive values.
shape the shape parameter xi.

Details

See gev, the VGAM family function for estimating the two parameters by maximum likelihood estimation, for formulae and other details. Apart from n, all the above arguments may be vectors and are recyled to the appropriate length if necessary.

Value

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

Note

The default value of xi=0 means the default distribution is the Gumbel.

Currently, these functions have different argument names compared with those in the evd package.

Author(s)

T. W. Yee

References

Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

See Also

gev.

Examples

## Not run: 
x = seq(-3, 3, by=0.01)
loc = 0; sigma = 1; xi = -0.4
plot(x, dgev(x, loc, sigma, xi), type="l", col="blue", ylim=c(0,1),
     main="Blue is density, red is cumulative distribution function",
     sub="Purple are 5,10,...,95 percentiles", ylab="", las=1)
abline(h=0, col="blue", lty=2)
lines(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), 
      dgev(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi),
      col="purple", lty=3, type="h")
lines(x, pgev(x, loc, sigma, xi), type="l", col="red")
abline(h=0, lty=2)

pgev(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi)
## End(Not run)

[Package VGAM version 0.7-7 Index]