fpot(x, threshold, model = c("gpd", "pp"), start, npp = length(x),
cmax = FALSE, r = 1, ulow = -Inf, rlow = 1, mper = NULL, ...,
std.err = TRUE, corr = FALSE, method = "BFGS", warn.inf = TRUE)"gpd" (the default) or
"pp", for the Generalized Pareto or Point Process
representations respectively.start is omitted the routine attempts to find good
starting values using moment estimators.npp observations per
``period'', where the return level plot produced by
plot.pot will represent return periods in units of
``periods''. By default npp = length(x), so that the
FALSE (the default), the model
is fitted using all exceedences over the threshold. If
TRUE, the model is fitted using cluster maxima, using
clusters of exceedences derived from clusters.clusters).
Ignored if cmax is FALSE (the default).NULL (the default),
or a positive number (see Details).
If mper is not NULL and model = "pp",
an erroptim. If parameters
of the model are included they will be held fixed at the
values given (see Examples).TRUE (the default), the standard
errors are returned.TRUE, the correlation matrix is
returned.optim for
details).TRUE (the default), a warning is
given if the negative log-likelihood is infinite when evaluated at
the starting values.c("pot","uvevd","pot"). The generic accessor functions fitted (or
fitted.values), std.errors,
deviance, logLik and
AIC extract various features of the
returned object.
The function profile can be
used to obtain deviance profiles for the model parameters.
In particular, profiles of the $m$ period
return level $z_m$ can be calculated and plotted when
$\code{mper} = m$.
The function anova compares nested models.
The function plot produces diagnostic plots.
An object of class c("pot","uvevd","pot") is a list containing
the following components
optim.cmax is
FALSE) or the number of clusters of exceedences (if
cmax is TRUE).nhigh divided by nat). If cmax is
FALSE, this is NULL.x.mper.mper is NULL and model = "gpd"
(the defaults), this will also be an element of param.threshold (if cmax is
FALSE) or the maxima of the clusters of exeedances (if
cmax is TRUE) are (if model = "gpd") fitted to a
generalized Pareto distribution (GPD) with location threshold.
If model = "pp" the exceedances are fitted to a
non-homogeneous Poisson process (Coles, 2001).
If mper is NULL (the default), the parameters of
the model (if model = "gpd") are scale and
shape, for the scale and shape parameters of the GPD.
If model = "pp" the parameters are loc, scale
and shape. Under model = "pp" the parameters can be
interpreted as parameters of the Generalized Extreme Value
distribution, fitted to the maxima of npp random variables.
In this case, the value of npp should be reasonably large.For both characterizations, the shape parameters are equivalent. The scale parameter under the generalized Pareto characterization is equal to $b + s(u - a)$, where $a$, $b$ and $s$ are the location, scale and shape parameters under the Point Process characterization, and where $u$ is the threshold.
If $\code{mper} = m$ is a positive value, then
the generalized Pareto model is reparameterized so that the
parameters are rlevel and shape, where
rlevel is the $m$ ``period'' return level, where
``period'' is defined via the argument npp.
The $m$ ``period'' return level is defined as follows.
Let $G$ be the fitted generalized Pareto distribution
function, with location $\code{threshold} = u$, so that
$1 - G(z)$ is the fitted probability of an exceedance
over $z > u$ given an exceedance over $u$.
The fitted probability of an exceedance over $z > u$ is
therefore $p(1 - G(z))$, where $p$ is the estimated
probabilty of exceeding $u$, which is given by the empirical
proportion of exceedances.
The $m$ ``period'' return level $z_m$ satisfies
$p(1 - G(z_m)) = 1/(mN)$, where $N$ is the number
of points per period (multiplied by the estimate of the
extremal index, if cluster maxima are fitted).
In other words, $z_m$ is the quantile of the fitted model
that corresponds to the upper tail probability $1/(mN)$.
If mper is infinite, then $z_m$ is the upper end point,
given by threshold minus $\code{scale}/\code{shape}$,
and the shape parameter is then restricted to be negative.
anova.evd, optim,
plot.uvevd, profile.evd,
profile2d.evd, mrlplot,
tcplotuvdata <- rgpd(100, loc = 0, scale = 1.1, shape = 0.2)
M1 <- fpot(uvdata, 1)
M2 <- fpot(uvdata, 1, shape = 0)
anova(M1, M2)
par(mfrow = c(2,2))
plot(M1)
M1P <- profile(M1)
plot(M1P)
M1 <- fpot(uvdata, 1, mper = 10)
M2 <- fpot(uvdata, 1, mper = 100)
M1P <- profile(M1, which = "rlevel", conf=0.975, mesh=0.1)
M2P <- profile(M2, which = "rlevel", conf=0.975, mesh=0.1)
plot(M1P)
plot(M2P)Run the code above in your browser using DataLab