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, log=FALSE, tolshape0 = sqrt(.Machine$double.eps), oobounds.log = -Inf, giveWarning=FALSE) 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.
If length(n) > 1 then the length is taken to be the number required. |
location |
the location parameter mu. |
scale |
the (positive) scale parameter sigma. |
shape |
the shape parameter xi. |
log |
Logical.
If log=TRUE then the logarithm of the density is returned.
|
tolshape0 |
Positive numeric.
Threshold/tolerance value for resting whether xi is zero.
If the absolute value of the estimate of xi is less than
this value then it will be assumed zero and an exponential distribution will
be used.
|
oobounds.log, giveWarning |
Numeric and logical.
The GPD distribution has support in the region satisfying
(x-location)/scale > 0
and
1+shape*(x-location)/scale > 0 .
Outside that region, the
logarithm of the density is assigned oobounds.log , which
equates to a zero density.
It should not be assigned a positive number, and ideally is very negative.
Since gpd uses this function it is necessary
to return a finite value outside this region so as to allow
for half-stepping. Both arguments are in support of this.
This argument and others match those of gpd .
|
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)