gpdUC {VGAM}R Documentation

The Generalized Pareto Distribution

Description

Density, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with location parameter location, scale parameter scale and shape parameter shape.

Usage

dgpd(x, location=0, scale=1, shape=0)
pgpd(q, location=0, scale=1, shape=0)
qgpd(p, location=0, scale=1, shape=0)
rgpd(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.
shape the shape parameter xi.

Details

See gpd, 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

dgpd gives the density, pgpd gives the distribution function, qgpd gives the quantile function, and rgpd generates random deviates.

Note

The default values of all three parameters, especially xi=0, means the default distribution is the exponential.

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

gpd.

Examples

## Not run: 
x = seq(-0.2, 3, by=0.01)
loc = 0; sigma = 1; xi = -0.4
plot(x, dgpd(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(qgpd(seq(0.05,0.95,by=0.05), loc, sigma, xi), 
      dgpd(qgpd(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi),
      col="purple", lty=3, type="h")
lines(x, pgpd(x, loc, sigma, xi), type="l", col="red")
abline(h=0, lty=2)
## End(Not run)

[Package VGAM version 0.7-7 Index]