gpdUC {VGAM} | R Documentation |
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
.
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)
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. |
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.
dgpd
gives the density,
pgpd
gives the distribution function,
qgpd
gives the quantile function, and
rgpd
generates random deviates.
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.
T. W. Yee
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
gpd
.
## 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)