gpdQPlot estimation of high quantiles,
gpdQuantPlot variation of high quantiles with threshold,
gpdRiskMeasures prescribed quantiles and expected shortfalls,
gpdSfallPlot expected shortfall with confidence intervals,
gpdShapePlot variation of shape with threshold,
gpdTailPlot plot of the tail,
tailPlot ,
tailSlider ,
tailRisk . }gpdQPlot(x, p = 0.99, ci = 0.95, type = c("likelihood", "wald"),
like.num = 50)
gpdQuantPlot(x, p = 0.99, ci = 0.95, models = 30, start = 15, end = 500,
doplot = TRUE, plottype = c("normal", "reverse"), labels = TRUE, ...)
gpdSfallPlot(x, p = 0.99, ci = 0.95, like.num = 50)
gpdShapePlot(x, ci = 0.95, models = 30, start = 15, end = 500,
doplot = TRUE, plottype = c("normal", "reverse"), labels = TRUE, ...)
gpdTailPlot(object, plottype = c("xy", "x", "y", ""), doplot = TRUE,
extend = 1.5, labels = TRUE, ...)gpdRiskMeasures(object, prob = c(0.99, 0.995, 0.999, 0.9995, 0.9999))
tailPlot(object, p = 0.99, ci = 0.95, nLLH = 25, extend = 1.5, labels = TRUE, ...)
tailSlider(x)
tailRisk(object, prob = c(0.99, 0.995, 0.999, 0.9995, 0.9999), ...)
"gpdFit".TRUE) or number
of extremes (FALSE)."mle" for the maximum likelihood mehtod or "pwm" for
the probability weighted moment method. By default, the first will
be selected. Notx and data depending
which function name is used, either gpdFitcontrol argument of
optim.gpdSim
returns a vector of datapoints from the simulated
series.
gpdFit
returns an object of class "gpd" describing the
fit including parameter estimates and standard errors.
gpdQuantPlot
returns invisible a table of results.
gpdShapePlot
returns invisible a table of results.
gpdTailPlot
returns invisible a list object containing
details of the plot is returned invisibly. This object should be
used as the first argument of gpdqPlot or gpdsfallPlot
to add quantile estimates or expected shortfall estimates to the
plot.gpdSim simulates data from a Generalized Pareto
distribution.
Parameter Estimation:
gpdFit fits the model parameters either by the probability
weighted moment method or the maxim log likelihood method.
The function returns an object of class "gpd"
representing the fit of a generalized Pareto model to excesses over
a high threshold. The fitting functions use the probability weighted
moment method, if method method="pwm" was selected, and the
the general purpose optimization function optim when the
maximum likelihood estimation, method="mle" or method="ml"
is chosen.
Methods:
print.gpd, plot.gpd and summary.gpd are print,
plot, and summary methods for a fitted object of class gpdFit.
The plot method provides four different plots for assessing fitted
GPD model.
gpd* Functions:
gpdqPlot calculates quantile estimates and confidence intervals
for high quantiles above the threshold in a GPD analysis, and adds a
graphical representation to an existing plot. The GPD approximation in
the tail is used to estimate quantile. The "wald" method uses
the observed Fisher information matrix to calculate confidence interval.
The "likelihood" method reparametrizes the likelihood in terms
of the unknown quantile and uses profile likelihood arguments to
construct a confidence interval.
gpdquantPlot creates a plot showing how the estimate of a
high quantile in the tail of a dataset based on the GPD approximation
varies with threshold or number of extremes. For every model
gpdFit is called. Evaluation may be slow. Confidence intervals
by the Wald method may be fastest.
gpdriskmeasures makes a rapid calculation of point estimates
of prescribed quantiles and expected shortfalls using the output of the
function gpdFit. This function simply calculates point estimates
and (at present) makes no attempt to calculate confidence intervals for
the risk measures. If confidence levels are required use gpdqPlot
and gpdsfallPlot which interact with graphs of the tail of a loss
distribution and are much slower.
gpdsfallPlot calculates expected shortfall estimates, in other
words tail conditional expectation and confidence intervals for high
quantiles above the threshold in a GPD analysis. A graphical
representation to an existing plot is added. Expected shortfall is
the expected size of the loss, given that a particular quantile of the
loss distribution is exceeded. The GPD approximation in the tail is used
to estimate expected shortfall. The likelihood is reparametrised in
terms of the unknown expected shortfall and profile likelihood arguments
are used to construct a confidence interval.
gpdshapePlot creates a plot showing how the estimate of shape
varies with threshold or number of extremes. For every model
gpdFit is called. Evaluation may be slow.
gpdtailPlot produces a plot of the tail of the underlying
distribution of the data.## Load Data:
danish = as.timeSeries(data(danishClaims))
## Tail Plot:
x = as.timeSeries(data(danishClaims))
fit = gpdFit(x, u = 10)
tailPlot(fit)
## Try Tail Slider:
# tailSlider(x)
## Tail Risk:
tailRisk(fit)Run the code above in your browser using DataLab