A collection and description functions to estimate
the parameters of the GEV distribution. To model
the GEV three types of approaches for parameter
estimation are provided: Maximum likelihood
estimation, probability weighted moment method,
and estimation by the MDA approach. MDA includes
functions for the Pickands, Einmal-Decker-deHaan,
and Hill estimators together with several plot
variants.
Maximum Domain of Attraction estimators:
hillPlot | shape parameter and Hill estimate of the tail index, |
shaparmPlot | variation of shape parameter with tail depth. |
hillPlot(x, start = 15, ci = 0.95,
doplot = TRUE, plottype = c("alpha", "xi"), labels = TRUE, ...)
shaparmPlot(x, p = 0.01*(1:10), xiRange = NULL, alphaRange = NULL,
doplot = TRUE, plottype = c("both", "upper"))
shaparmPickands(x, p = 0.05, xiRange = NULL,
doplot = TRUE, plottype = c("both", "upper"), labels = TRUE, ...)
shaparmHill(x, p = 0.05, xiRange = NULL,
doplot = TRUE, plottype = c("both", "upper"), labels = TRUE, ...)
shaparmDEHaan(x, p = 0.05, xiRange = NULL,
doplot = TRUE, plottype = c("both", "upper"), labels = TRUE, ...)gevSim
returns a vector of data points from the simulated series.
gevFit
returns an object of class gev describing the fit.
print.summary
prints a report of the parameter fit.
summary
performs diagnostic analysis. The method provides two different residual plots for assessing the fitted GEV model.
gevrlevelPlot
returns a vector containing the lower 95% bound of the confidence interval, the estimated return level and the upper 95% bound.
hillPlot
displays a plot.
shaparmPlot
returns a list with one or two entries, depending on the
selection of the input variable both.tails. The two
entries upper and lower determine the position of
the tail. Each of the two variables is again a list with entries
pickands, hill, and dehaan. If one of the
three methods will be discarded the printout will display zeroes.
[saparmPlot] -
plotting ranges for alpha and xi. By default the
values are automatically selected.
[hillPlot] -
probability for asymptotic confidence band; for no
confidence band set ci to zero.
a logical. Should the results be plotted?
[shaparmPlot] -
a vector of logicals of the same lengths as tails
defining for which tail depths plots should be created,
by default plots will be generated for a tail depth of 5
percent. By default c(FALSE, FALSE, FALSE, FALSE,
TRUE, FALSE, FALSE, FALSE, FALSE, FALSE).
[hillPlot] -
whether or not axes should be labelled.
[hillPlot] -
whether alpha, xi (1/alpha) or
quantile (a quantile estimate) should be plotted.
[qgev] -
a numeric vector of probabilities.
[hillPlot] -
probability required when option quantile is
chosen.
[hillPlot] -
lowest number of order statistics at which to plot
a point.
[dgev][devd] -
a numeric vector of quantiles.
[gevFit] -
data vector. In the case of method="mle" the interpretation
depends on the value of block: if no block size is specified then
data are interpreted as block maxima; if block size is set, then data
are interpreted as raw data and block maxima are calculated.
[hillPlot][shaparmPlot] -
the data from which to calculate the shape parameter, a
numeric vector.
[print][plot] -
a fitted object of class "gevFit".
[gevFit] -
control parameters optionally passed to the
optimization function. Parameters for the optimization
function are passed to components of the control argument of
optim.
[hillPlot] -
other graphics parameters.
[plot][summary] -
arguments passed to the plot function.
Alec Stephenson for R's evd and evir package, and
Diethelm Wuertz for this R-port.
Parameter Estimation:
gevFit and gumbelFit estimate the parameters either
by the probability weighted moment method, method="pwm" or
by maximum log likelihood estimation method="mle". The
summary method produces diagnostic plots for fitted GEV or Gumbel
models.
Methods:
print.gev, plot.gev and summary.gev are
print, plot, and summary methods for a fitted object of class
gev. Concerning the summary method, the data are
converted to unit exponentially distributed residuals under null
hypothesis that GEV fits. Two diagnostics for iid exponential data
are offered. The plot method provides two different residual plots
for assessing the fitted GEV model. Two diagnostics for
iid exponential data are offered.
Return Level Plot:
gevrlevelPlot calculates and plots the k-block return level
and 95% confidence interval based on a GEV model for block maxima,
where k is specified by the user. The k-block return level
is that level exceeded once every k blocks, on average. The
GEV likelihood is reparameterized in terms of the unknown return
level and profile likelihood arguments are used to construct a
confidence interval.
Hill Plot:
The function hillPlot investigates the shape parameter and
plots the Hill estimate of the tail index of heavy-tailed data, or
of an associated quantile estimate. This plot is usually calculated
from the alpha perspective. For a generalized Pareto analysis of
heavy-tailed data using the gpdFit function, it helps to
plot the Hill estimates for xi.
Shape Parameter Plot:
The function shaparmPlot investigates the shape parameter and
plots for the upper and lower tails the shape parameter as a function
of the taildepth. Three approaches are considered, the Pickands
estimator, the Hill estimator, and the
Decker-Einmal-deHaan estimator.
Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.
## Load Data:
library(timeSeries)
x = as.timeSeries(data(danishClaims))
colnames(x) <- "Danish"
head(x)
## hillPlot -
# Hill plot of heavy-tailed Danish fire insurance data
par(mfrow = c(1, 1))
hillPlot(x, plottype = "xi")
grid()
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