emdPlot Plot of empirical distribution function,
qqparetoPlot Exponential/Pareto quantile plot,
mePlot Plot of mean excesses over a threshold,
mrlPlot another variant, mean residual life plot,
mxfPlot another variant, with confidence intervals,
msratioPlot Plot of the ratio of maximum and sum,
recordsPlot Record development compared with iid data,
ssrecordsPlot another variant, investigates subsamples,
sllnPlot verifies Kolmogorov's strong law of large numbers,
lilPlot verifies Hartman-Wintner's law of the iterated logarithm,
xacfPlot ACF of exceedences over a threshold. }emdPlot(x, doplot = TRUE, plottype = c("xy", "x", "y", " "),
labels = TRUE, ...)qqparetoPlot(x, xi = 0, trim = NULL, threshold = NULL, doplot = TRUE,
labels = TRUE, ...)
mePlot(x, doplot = TRUE, labels = TRUE, ...)
mrlPlot(x, ci = 0.95, umin = mean(x), umax = max(x), nint = 100, doplot = TRUE,
plottype = c("autoscale", ""), labels = TRUE, ...)
mxfPlot(x, u = quantile(x, 0.05), doplot = TRUE, labels = TRUE, ...)
msratioPlot(x, p = 1:4, doplot = TRUE, labels = TRUE, ...)
recordsPlot(x, ci = 0.95, doplot = TRUE, labels = TRUE, ...)
ssrecordsPlot(x, subsamples = 10, doplot = TRUE, plottype = c("lin", "log"),
labels = TRUE, ...)
sllnPlot(x, doplot = TRUE, labels = TRUE, ...)
lilPlot(x, doplot = TRUE, labels = TRUE, ...)
xacfPlot(x, u = quantile(x, 0.95), lag.max = 15, doplot = TRUE,
which = c("all", 1, 2, 3, 4), labels = TRUE, ...)
TRUE.TRUE.umin and umax. The
default value is 100."x" x-axis only;
"y" y-axis only; "xy" both axes; ""
neither axis.
[msratioPlot] -
a logical, if set to "autoscale"u=quantile(x,0.95).umin and/or umax are
not available, then by default they are set to the following
values: umin=mean(x) and umax=max(x).which="all" then all
four plots are displayed, if which is an integer between
one and four, then the first, second, third or fourth plot will
be displayed.emdPlot is a simple explanatory function. A
straight line on the double log scale indicates Pareto tail behaviour.
Quantile--Quantile Pareto Plot:
qqparetoPlot creates a quantile-quantile plot for threshold
data. If xi is zero the reference distribution is the
exponential; if xi is non-zero the reference distribution
is the generalized Pareto with that parameter value expressed
by xi. In the case of the exponential, the plot is
interpreted as follows: Concave departures from a straight line are a
sign of heavy-tailed behaviour, convex departures show thin-tailed
behaviour.
Mean Excess Function Plot:
Three variants to plot the mean excess function are available:
A sample mean excess plot over increasing thresholds, and two mean
excess function plots with confidence intervals for discrimination
in the tails of a distribution.
In general, an upward trend in a mean excess function plot shows
heavy-tailed behaviour. In particular, a straight line with positive
gradient above some threshold is a sign of Pareto behaviour in tail.
A downward trend shows thin-tailed behaviour whereas a line with
zero gradient shows an exponential tail. Here are some hints:
Because upper plotting points are the average of a handful of extreme
excesses, these may be omitted for a prettier plot.
For mrlPlot and mxfPlot the upper tail is investigated;
for the lower tail reverse the sign of the data vector.
Plot of the Maximum/Sum Ratio:
The ratio of maximum and sum is a simple tool for detecting heavy
tails of a distribution and for giving a rough estimate of
the order of its finite moments. Sharp increases in the curves
of a msratioPlot are a sign for heavy tail behaviour.
Plot of the Development of Records:
These are functions that investigate the development of records in
a dataset and calculate the expected behaviour for iid data.
recordsPlot counts records and reports the observations
at which they occur. In addition subsamples can be investigated
with the help of the function ssrecordsPlot.
Plot of Kolmogorov's and Hartman-Wintern's Laws:
The function sllnPlot verifies Kolmogorov's strong law of
large numbers, and the function lilPlot verifies
Hartman-Wintner's law of the iterated logarithm.
ACF Plot of Exceedences over a Thresold:
This function plots the autocorrelation functions of heights and
distances of exceedences over a threshold.## Danish fire insurance data:
data(danishClaims)
danishClaims = as.timeSeries(danishClaims)
## emdPlot -
# Show Pareto tail behaviour:
par(mfrow = c(2, 2), cex = 0.7)
emdPlot(danishClaims)
## qqparetoPlot -
# QQ-Plot of heavy-tailed Danish fire insurance data:
qqparetoPlot(danishClaims, xi = 0.7)
## mePlot -
# Sample mean excess plot of heavy-tailed Danish fire:
mePlot(danishClaims)
## ssrecordsPlot -
# Record fire insurance losses in Denmark:
ssrecordsPlot(danishClaims, subsamples = 10)Run the code above in your browser using DataLab