VGAM (version 0.7-8)

gpdUC: 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 $\xi$.

Value

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

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.

References

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

See Also

gpd.

Examples

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)