gevUC {VGAM} | R Documentation |
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
.
dgev(x, location=0, scale=1, shape=0, log=FALSE, tolshape0 = sqrt(.Machine$double.eps), oobounds.log = -Inf, giveWarning = FALSE) pgev(q, location=0, scale=1, shape=0) qgev(p, location=0, scale=1, shape=0) rgev(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. Must consist of positive values. |
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 a Gumbel distribution will
be used.
|
oobounds.log, giveWarning |
Numeric and logical.
The GEV distribution has support in the region satisfying
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 egev 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 egev .
|
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.
dgev
gives the density,
pgev
gives the distribution function,
qgev
gives the quantile function, and
rgev
generates random deviates.
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.
T. W. Yee
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
gev
,
egev
,
vglm.control
.
## 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)