A collection and description of functions for
explorative data analysis. The tools include
plot functions for empirical distributions, quantile
plots, graphs exploring the properties of exceedances
over a threshold, plots for mean/sum ratio and for
the development of records.
The functions are:
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 exceedances over a threshold, |
normMeanExcessFit | fits mean excesses with a normal density, |
ghMeanExcessFit | fits mean excesses with a GH density, |
hypMeanExcessFit | fits mean excesses with a HYP density, |
nigMeanExcessFit | fits mean excesses with a NIG density, |
ghtMeanExcessFit | fits mean excesses with a GHT density. |
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, ...)
normMeanExcessFit(x, doplot = TRUE, trace = TRUE, ...)
ghMeanExcessFit(x, doplot = TRUE, trace = TRUE, ...)
hypMeanExcessFit(x, doplot = TRUE, trace = TRUE, ...)
nigMeanExcessFit(x, doplot = TRUE, trace = TRUE, ...)
ghtMeanExcessFit(x, doplot = TRUE, trace = TRUE, ...)
The functions return a plot.
[recordsPlot] -
a confidence level. By default 0.95, i.e. 95%.
a logical value. Should the results be plotted? By
default TRUE.
a logical value. Whether or not x- and y-axes should be automatically
labelled and a default main title should be added to the plot.
By default TRUE.
[xacfPlot] -
maximum number of lags at which to calculate the autocorrelation
functions. The default value is 15.
[mrlPlot] -
the number of intervals, see umin and umax. The
default value is 100.
[msratioPlot] -
the power exponents, a numeric vector. By default a sequence from
1 to 4 in unit integer steps.
[emdPlot] -
which axes should be on a log scale: "x" x-axis only;
"y" y-axis only; "xy" both axes; ""
neither axis.
[msratioPlot] -
a logical, if set to "autoscale", then the scale of the
plots are automatically determined, any other string allows user
specified scale information through the ... argument.
[ssrecordsPlot] -
one from two options can be select either "lin"
or "log". The default creates a linear plot.
[ssrecordsPlot] -
the number of subsamples, by default 10, an integer value.
[qPlot][xacfPlot] -
a numeric value at which data are to be left-truncated, value
at which data are to be right-truncated or the threshold value,
by default 95%.
a logical flag, by default TRUE. Should the calculations
be traced?
a numeric value at which level the data are to be truncated. By
default the threshold value which belongs to the 95% quantile,
u=quantile(x,0.95).
[mrlPlot] -
range of threshold values. If umin and/or umax are
not available, then by default they are set to the following
values: umin=mean(x) and umax=max(x).
[xacfPlot] -
a numeric or character value, if 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.
numeric data vectors or in the case of x an object to be plotted.
the shape parameter of the generalized Pareto distribution.
additional arguments passed to the FUN or plot function.
Some of the functions were implemented from Alec Stephenson's
R-package evir ported from Alexander McNeil's S library
EVIS, Extreme Values in S, some from Alec Stephenson's
R-package ismev based on Stuart Coles code from his book,
Introduction to Statistical Modeling of Extreme Values and
some were written by Diethelm Wuertz.
Empirical Distribution Function:
The function 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-Wintner'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 Exceedances over a Threshold:
This function plots the autocorrelation functions of heights and
distances of exceedances over a threshold.
Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.
## Danish fire insurance data:
data(danishClaims)
library(timeSeries)
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)
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