Mean excess plot
The Mean Excess plot is a graphical method for detecting the threshold (scale parameter) of a Pareto distribution.
meanExcessPlot(x, w = NULL, probs = NULL, interactive = TRUE,
pch = par("pch"), cex = par("cex"), col = par("col"),
bg = "transparent", ...)x |
a numeric vector. |
w |
an optional numeric vector giving sample weights. |
probs |
an optional numeric vector of probabilities with values in [0,1], defining the quantiles to be plotted. This is useful for large data sets, when it may not be desirable to plot every single point. |
interactive |
a logical indicating whether the threshold (scale parameter) can be selected interactively by clicking on points. Information on the selected threshold is then printed on the console. |
pch, cex, col, bg |
graphical parameters for the plot symbol of each data
point or quantile (see |
... |
additional arguments to be passed to
|
The corresponding mean excesses are plotted against the values of x
(if supplied, only those specified by probs). If the tail of the data
follows a Pareto distribution, these observations show a positive linear
trend. The leftmost point of a fitted line can thus be used as an estimate of
the threshold (scale parameter).
The interactive selection of the threshold (scale parameter) is implemented
using identify. For the usual X11 device, the
selection process is thus terminated by pressing any mouse button other than
the first. For the quartz device (on Mac OS X systems), the process
is terminated either by a secondary click (usually second mouse button or
Ctrl-click) or by pressing the ESC key.
If interactive is TRUE, the last selection for the
threshold is returned invisibly as an object of class "paretoScale",
which consists of the following components:
x0 |
the selected threshold (scale parameter). |
k |
the number of observations in the tail (i.e., larger than the threshold). |
The functionality to account for sample weights and to select the threshold (scale parameter) interactively was introduced in version 0.2.
Andreas Alfons and Josef Holzer
data(eusilc) # equivalized disposable income is equal for each household # member, therefore only one household member is taken eusilc <- eusilc[!duplicated(eusilc$db030),] # with sample weights meanExcessPlot(eusilc$eqIncome, w = eusilc$db090) # without sample weights meanExcessPlot(eusilc$eqIncome)
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